Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 2

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Let $α, β$ be the roots of $a x^{2} + b x + c = 0, γ, δ$ be the roots of $p x^{2} + q x + r = 0$ and $D_{1}$ and $D_{2}$ be their respective discriminant. If $α, β, γ, δ$ are in A.P., then the ratio $D_{1} : D_{2}$ is equal to

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Important Questions on Quadratic Equations

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 3

The value of

k

if

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 4

If the difference of the roots of the equation

x^{2} + a x + b = 0

is equal to the difference of the roots of the equation

x^{2} + b x + a = 0,

then

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 5

If the equations

p x^{2} + 2 q x + r = 0

and

p x^{2} + 2 r x + q = 0 (q \neq r)

have a common root, then

p + 4 q + 4 r

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 6

Consider that

f (x) = a x^{2} + b x + c, D = b^{2} - 4 a c,

then which of the following is not true ?

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 8

If

p, q, r

are real numbers satisfying the condition

p + q + r = 0,

then the roots of the quadratic equation

3 p x^{2} + 5 q x + 7 r = 0

are

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 9

If

x

is real, then the expression

\frac{x^{2} + 34 x - 71}{x^{2} + 2 x - 7}

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 10

Let

a, b, c \in R

and

a \neq 0

be such that

(a + c)^{2} < b^{2},

then the quadratic equation

a x^{2} + b x + c = 0

has

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 12

The roots of

a x^{2} + b x + c = 0

, whose

a \neq 0,

b,

c \in R,

are non-real complex and

a + c < b .

Then