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

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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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Important Questions on Quadratic Equations

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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

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 13

The number of irrational roots of the equation

(x - 1) (x - 2) (3 x - 2) (3 x + 1) = 21

is

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 14

If

α, β

are the roots of the equation

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

then equation

{(a + c y)}^{2} = b^{2} y

in

y

has the roots

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 15

If

a, b, c

are in

G . P .,

then the equation

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

and

d x^{2} + 2 e x + f = 0

have a common root if

\frac{d}{a}, \frac{e}{b}, \frac{f}{c}

are in

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 16

If

a < b < c < d

and

k > 0,

then the quadratic equation

(x - a) (x - c) + k (x - b) (x - d) = 0

has