Quadratic Equations Questions

MathematicsQuadratic Equations90 Questions Found

MathematicsRelation Between Roots and CoefficientsJEE Advanced 1990Easy

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If $x < 0, y < 0, x + y + \frac{x}{y} = \frac{1}{2}$ and $(x + y) \frac{x}{y} = - \frac{1}{2}$ , then $x = \dots$ and $y = \dots$

Answer:-1/4, -1/4

MathematicsRelation Between Roots and CoefficientsJEE Advanced 1996Easy

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The real numbers $x_{1}, x_{2}, x_{3}$ satisfying the equation $x^{3} - x^{2} + β x + γ = 0$ are in AP. Find the intervals in which $β$ and $γ$ lie.

Answer:

β \in (- \infty, 1/3], γ \in [- 1/27, \infty)

MathematicsRelation Between Roots and CoefficientsJEE Advanced 1997Moderate

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Let $p$ and $q$ be roots of the equation $x^{2} - A x + A = 0$ and let $r$ and $s$ be the roots of the equation $x^{2} - 18 x + B = 0$ . If $p < q < r < s$ are in arithmetic progression, then $A = \dots$ and $B = \dots$ .

Answer:-3, 77

MathematicsRelation Between Roots and CoefficientsJEE Advanced 2001Easy

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Let $a, b, c$ be real numbers with $a \neq = 0$ and let $α, β$ be the roots of the equation $a x^{2} + b x + c = 0$ . Express the roots of $a^{3} x^{2} + ab c x + c^{3} = 0$ in terms of $α, β$ .

Answer:

α^{2} β, α β^{2}

MathematicsNature of RootsJEE Advanced 2003Easy

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If $x^{2} + (a - b) x + (1 - a - b) = 0$ where $a, b \in R$ then find the values of $a$ for which equation has unequal real roots for all values of $b$ .

Answer:

a > 1

MathematicsMaximum and Minimum Values of Quadratic ExpressionsJEE Advanced 2005Moderate

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Find the range of values of $t$ for which $2 sin t = \frac{1 - 2 x + 5 x ^{2}}{3 x ^{2} - 2 x - 1}$ , $t \in [- π /2, π /2]$ .

Answer:

[- \frac{π}{2}, - \frac{π}{10}] \cup [\frac{3 π}{10}, \frac{π}{2}]

MathematicsSolution of Quadratic EquationsJEE Advanced 1978Easy

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Find all integers $x$ for which $(5 x - 1) < (x + 1)^{2} < (7 x - 3)$ .

Answer:3

MathematicsSolution of Quadratic EquationsJEE Advanced 1978Easy

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Solve for $x : x + 1 - x - 1 = 1$ .

Answer:1.25

MathematicsRelation Between Roots and CoefficientsJEE Advanced 1982Easy

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The coefficient of $x^{99}$ in the polynomial $(x - 1) (x - 2) \dots (x - 100)$ is .........

Answer:-5050

MathematicsRelation Between Roots and CoefficientsJEE Advanced 1984Easy

View in:English Hindi

If the product of the roots of the equation $x^{2} - 3 k x + 2 e^{2 l n k} - 1 = 0$ is $7$ , then the roots are real for $k = \dots$

Answer:2

...9

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If x<0,y<0,x+y+yx​=21​ and (x+y)yx​=−21​, then x=… and y=…

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The real numbers x1​,x2​,x3​ satisfying the equation x3−x2+βx+γ=0 are in AP. Find the intervals in which β and γ lie.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let p and q be roots of the equation x2−Ax+A=0 and let r and s be the roots of the equation x2−18x+B=0. If p<q<r<s are in arithmetic progression, then A=… and B=….

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let a,b,c be real numbers with a=0 and let α,β be the roots of the equation ax2+bx+c=0. Express the roots of a3x2+abcx+c3=0 in terms of α,β.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If x2+(a−b)x+(1−a−b)=0 where a,b∈R then find the values of a for which equation has unequal real roots for all values of b.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find the range of values of t for which 2sint=3x2−2x−11−2x+5x2​, t∈[−π/2,π/2].

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find all integers x for which (5x−1)<(x+1)2<(7x−3).

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Solve for x:x+1​−x−1​=1.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The coefficient of x99 in the polynomial (x−1)(x−2)…(x−100) is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the product of the roots of the equation x2−3kx+2e2lnk−1=0 is 7, then the roots are real for k=…

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If x<0,y<0,x+y+yx​=21​ and (x+y)yx​=−21​, then x=… and y=…

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The real numbers x1​,x2​,x3​ satisfying the equation x3−x2+βx+γ=0 are in AP. Find the intervals in which β and γ lie.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let p and q be roots of the equation x2−Ax+A=0 and let r and s be the roots of the equation x2−18x+B=0. If p<q<r<s are in arithmetic progression, then A=… and B=….

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let a,b,c be real numbers with a=0 and let α,β be the roots of the equation ax2+bx+c=0. Express the roots of a3x2+abcx+c3=0 in terms of α,β.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If x2+(a−b)x+(1−a−b)=0 where a,b∈R then find the values of a for which equation has unequal real roots for all values of b.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find the range of values of t for which 2sint=3x2−2x−11−2x+5x2​, t∈[−π/2,π/2].

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find all integers x for which (5x−1)<(x+1)2<(7x−3).

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Solve for x:x+1​−x−1​=1.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The coefficient of x99 in the polynomial (x−1)(x−2)…(x−100) is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the product of the roots of the equation x2−3kx+2e2lnk−1=0 is 7, then the roots are real for k=…

If $x < 0, y < 0, x + y + \frac{x}{y} = \frac{1}{2}$ and $(x + y) \frac{x}{y} = - \frac{1}{2}$ , then $x = \dots$ and $y = \dots$

The real numbers $x_{1}, x_{2}, x_{3}$ satisfying the equation $x^{3} - x^{2} + β x + γ = 0$ are in AP. Find the intervals in which $β$ and $γ$ lie.

Let $p$ and $q$ be roots of the equation $x^{2} - A x + A = 0$ and let $r$ and $s$ be the roots of the equation $x^{2} - 18 x + B = 0$ . If $p < q < r < s$ are in arithmetic progression, then $A = \dots$ and $B = \dots$ .

Let $a, b, c$ be real numbers with $a \neq = 0$ and let $α, β$ be the roots of the equation $a x^{2} + b x + c = 0$ . Express the roots of $a^{3} x^{2} + ab c x + c^{3} = 0$ in terms of $α, β$ .

If $x^{2} + (a - b) x + (1 - a - b) = 0$ where $a, b \in R$ then find the values of $a$ for which equation has unequal real roots for all values of $b$ .

Find the range of values of $t$ for which $2 sin t = \frac{1 - 2 x + 5 x ^{2}}{3 x ^{2} - 2 x - 1}$ , $t \in [- π /2, π /2]$ .

Find all integers $x$ for which $(5 x - 1) < (x + 1)^{2} < (7 x - 3)$ .

Solve for $x : x + 1 - x - 1 = 1$ .

The coefficient of $x^{99}$ in the polynomial $(x - 1) (x - 2) \dots (x - 100)$ is .........

If the product of the roots of the equation $x^{2} - 3 k x + 2 e^{2 l n k} - 1 = 0$ is $7$ , then the roots are real for $k = \dots$

If $x < 0, y < 0, x + y + \frac{x}{y} = \frac{1}{2}$ and $(x + y) \frac{x}{y} = - \frac{1}{2}$ , then $x = \dots$ and $y = \dots$

The real numbers $x_{1}, x_{2}, x_{3}$ satisfying the equation $x^{3} - x^{2} + β x + γ = 0$ are in AP. Find the intervals in which $β$ and $γ$ lie.

Let $p$ and $q$ be roots of the equation $x^{2} - A x + A = 0$ and let $r$ and $s$ be the roots of the equation $x^{2} - 18 x + B = 0$ . If $p < q < r < s$ are in arithmetic progression, then $A = \dots$ and $B = \dots$ .

Let $a, b, c$ be real numbers with $a \neq = 0$ and let $α, β$ be the roots of the equation $a x^{2} + b x + c = 0$ . Express the roots of $a^{3} x^{2} + ab c x + c^{3} = 0$ in terms of $α, β$ .

If $x^{2} + (a - b) x + (1 - a - b) = 0$ where $a, b \in R$ then find the values of $a$ for which equation has unequal real roots for all values of $b$ .

Find the range of values of $t$ for which $2 sin t = \frac{1 - 2 x + 5 x ^{2}}{3 x ^{2} - 2 x - 1}$ , $t \in [- π /2, π /2]$ .

Find all integers $x$ for which $(5 x - 1) < (x + 1)^{2} < (7 x - 3)$ .

Solve for $x : x + 1 - x - 1 = 1$ .

The coefficient of $x^{99}$ in the polynomial $(x - 1) (x - 2) \dots (x - 100)$ is .........

If the product of the roots of the equation $x^{2} - 3 k x + 2 e^{2 l n k} - 1 = 0$ is $7$ , then the roots are real for $k = \dots$