Quadratic Equations Questions

MathematicsQuadratic Equations90 Questions Found

MathematicsMaximum and Minimum Values of Quadratic ExpressionsJEE Main 2006Easy

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If $x$ is real, the maximum value of $\frac{3 x ^{2} + 9 x + 17}{3 x ^{2} + 9 x + 7}$ is

(A)

1/4

(B)

(C)

(D)

17/7

Answer:B

MathematicsLocation of RootsJEE Main 2006Easy

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All the values of $m$ for which both roots of the equation $x^{2} - 2 m x + m^{2} - 1 = 0$ are greater than - 2 but less than 4, lie in the interval

(A)

- 2 < m < 0

(B)

m > 3

(C)

- 1 < m < 3

(D)

1 < m < 4

Answer:C

MathematicsRelation Between Roots and CoefficientsJEE Main 2007Easy

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If the difference between the roots of the equation $x^{2} + a x + 1 = 0$ is less than $5$ , then the set of possible values of $a$ is

(A)

(3, \infty)

(B)

(- \infty, - 3)

(C)

(- 3, 3)

(D)

(- 3, \infty)

Answer:C

MathematicsMaximum and Minimum Values of Quadratic ExpressionsJEE Main 2009Easy

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If the roots of the equation $b x^{2} + c x + a = 0$ be imaginary, then for all real values of $x$ , the expression $3 b^{2} x^{2} + 6 b c x + 2 c^{2}$ is

(A)

less than

4 ab

(B)

greater than

- 4 ab

(C)

less than

- 4 ab

(D)

greater than

4 ab

Answer:B

MathematicsCommon RootsJEE Main 2009Easy

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The quadritic equations $x^{2} - 6 x + a = 0$ and $x^{2} - c x + 6 = 0$ have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

(A)

(B)

(C)

(D)

Answer:D

MathematicsCommon RootsJEE Main 2013Easy

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If the equations $x^{2} + 2 x + 3 = 0$ and $a x^{2} + b x + c = 0, a, b, c \in R$ , have a common root, then $a : b : c$ is

(A)

1 : 2 : 3

(B)

3 : 2 : 1

(C)

1 : 3 : 2

(D)

3 : 1 : 2

Answer:A

MathematicsRelation Between Roots and CoefficientsJEE Main 2014Moderate

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Let $α$ and $β$ be the roots of equation $p x^{2} + q x + r = 0, p \neq = 0$ . If $p, q, r$ are in A.P. and $1/ α + 1/ β = 4$ , then the value of $∣ α - β ∣$ is:

(A)

34 /9

(B)

2\sqrt{13} / 9$

(C)

61 /9

(D)

2\sqrt{17} / 9$

Answer:B

MathematicsMaximum and Minimum Values of Quadratic ExpressionsJEE Main 2014Moderate

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If $a \in R$ and the equation $- 3 (x - [x])^{2} + 2 (x - [x]) + a^{2} = 0$ (where $[x]$ denotes the greatest integer $\leq x$ ) has no integral solution, then all possible values of $a$ lie in the interval:

(A)

(- 2, - 1)

(B)

(- \infty, - 2) \cup (2, \infty)

(C)

(- 1, 0) \cup (0, 1)

(D)

(1, 2)

Answer:C

MathematicsRelation Between Roots and CoefficientsJEE Main 2015Easy

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Let $α$ and $β$ be the roots of equation $x^{2} - 6 x - 2 = 0$ . If $a_{n} = α^{n} - β^{n}$ , for $n \geq 1$ , then the value of $\frac{a _{10} - 2 a _{8}}{2 a _{9}}$ is equal to :

(A)

(B)

- 3

(C)

(D)

- 6

Answer:A

MathematicsSolution of Quadratic EquationsJEE Main 2016Easy

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The sum of all real values of $x$ satisfying the equation $(x^{2} - 5 x + 5)^{x^{2} + 4 x - 60} = 1$ is :

(A)

(B)

(C)

(D)

- 4

Answer:C

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.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If x is real, the maximum value of 3x2+9x+73x2+9x+17​ is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } All the values of m for which both roots of the equation x2−2mx+m2−1=0 are greater than - 2 but less than 4, lie in the interval

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the difference between the roots of the equation x2+ax+1=0 is less than 5​, then the set of possible values of a is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the roots of the equation bx2+cx+a=0 be imaginary, then for all real values of x, the expression 3b2x2+6bcx+2c2 is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the equations x2+2x+3=0 and ax2+bx+c=0,a,b,c∈R, have a common root, then a:b:c is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let α and β be the roots of equation px2+qx+r=0,p=0. If p,q,r are in A.P. and 1/α+1/β=4, then the value of ∣α−β∣ is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let α and β be the roots of equation x2−6x−2=0. If an​=αn−βn, for n≥1, then the value of 2a9​a10​−2a8​​ is equal to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The sum of all real values of x satisfying the equation (x2−5x+5)x2+4x−60=1 is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If x is real, the maximum value of 3x2+9x+73x2+9x+17​ is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } All the values of m for which both roots of the equation x2−2mx+m2−1=0 are greater than - 2 but less than 4, lie in the interval

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the difference between the roots of the equation x2+ax+1=0 is less than 5​, then the set of possible values of a is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the roots of the equation bx2+cx+a=0 be imaginary, then for all real values of x, the expression 3b2x2+6bcx+2c2 is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the equations x2+2x+3=0 and ax2+bx+c=0,a,b,c∈R, have a common root, then a:b:c is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let α and β be the roots of equation px2+qx+r=0,p=0. If p,q,r are in A.P. and 1/α+1/β=4, then the value of ∣α−β∣ is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let α and β be the roots of equation x2−6x−2=0. If an​=αn−βn, for n≥1, then the value of 2a9​a10​−2a8​​ is equal to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The sum of all real values of x satisfying the equation (x2−5x+5)x2+4x−60=1 is :

If $x$ is real, the maximum value of $\frac{3 x ^{2} + 9 x + 17}{3 x ^{2} + 9 x + 7}$ is

All the values of $m$ for which both roots of the equation $x^{2} - 2 m x + m^{2} - 1 = 0$ are greater than - 2 but less than 4, lie in the interval

If the difference between the roots of the equation $x^{2} + a x + 1 = 0$ is less than $5$ , then the set of possible values of $a$ is

If the roots of the equation $b x^{2} + c x + a = 0$ be imaginary, then for all real values of $x$ , the expression $3 b^{2} x^{2} + 6 b c x + 2 c^{2}$ is

If the equations $x^{2} + 2 x + 3 = 0$ and $a x^{2} + b x + c = 0, a, b, c \in R$ , have a common root, then $a : b : c$ is

Let $α$ and $β$ be the roots of equation $p x^{2} + q x + r = 0, p \neq = 0$ . If $p, q, r$ are in A.P. and $1/ α + 1/ β = 4$ , then the value of $∣ α - β ∣$ is:

Let $α$ and $β$ be the roots of equation $x^{2} - 6 x - 2 = 0$ . If $a_{n} = α^{n} - β^{n}$ , for $n \geq 1$ , then the value of $\frac{a _{10} - 2 a _{8}}{2 a _{9}}$ is equal to :

The sum of all real values of $x$ satisfying the equation $(x^{2} - 5 x + 5)^{x^{2} + 4 x - 60} = 1$ is :

If $x$ is real, the maximum value of $\frac{3 x ^{2} + 9 x + 17}{3 x ^{2} + 9 x + 7}$ is

All the values of $m$ for which both roots of the equation $x^{2} - 2 m x + m^{2} - 1 = 0$ are greater than - 2 but less than 4, lie in the interval

If the difference between the roots of the equation $x^{2} + a x + 1 = 0$ is less than $5$ , then the set of possible values of $a$ is

If the roots of the equation $b x^{2} + c x + a = 0$ be imaginary, then for all real values of $x$ , the expression $3 b^{2} x^{2} + 6 b c x + 2 c^{2}$ is

If the equations $x^{2} + 2 x + 3 = 0$ and $a x^{2} + b x + c = 0, a, b, c \in R$ , have a common root, then $a : b : c$ is

Let $α$ and $β$ be the roots of equation $p x^{2} + q x + r = 0, p \neq = 0$ . If $p, q, r$ are in A.P. and $1/ α + 1/ β = 4$ , then the value of $∣ α - β ∣$ is:

Let $α$ and $β$ be the roots of equation $x^{2} - 6 x - 2 = 0$ . If $a_{n} = α^{n} - β^{n}$ , for $n \geq 1$ , then the value of $\frac{a _{10} - 2 a _{8}}{2 a _{9}}$ is equal to :

The sum of all real values of $x$ satisfying the equation $(x^{2} - 5 x + 5)^{x^{2} + 4 x - 60} = 1$ is :