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Zeroes of a Polynomial

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Question

What is the value of ${a x}^{2} + b x + c$ at $x = \frac{- b}{a}$ ?

A

a

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B

b^{2} - 4 a c

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C

c

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D

0

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Solution

The correct option is C $c$
Given expression is $a x^{2} + b x + c$
For required value put $x = - \frac{b}{a}$ in the given expression,
$∴$ Required Value $= a {(\frac{- b}{a})}^{2} + b (\frac{- b}{a}) + c$
$= \frac{a \times b^{2}}{a^{2}} + \frac{b \times - b}{a} + c$

$= \frac{b^{2}}{a} - \frac{b^{2}}{a} + c$
$= c$ .

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Similar questions

Q. Assertion :If

a > 0

b^{2} - 4 a c < 0

, then the value of the integral

\int \frac{d x}{a x^{2} + b x + c}

will be of the type

μ {tan}^{- 1} \frac{x + A}{B} + C

A, B, C, μ

are constants. Reason: If

a > 0

b^{2} - 4 a c < 0

a x^{2} + b x + C

can be written as sum of two squares.

Q. What is the nature of the roots of the quadratic equation

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

b^{2} - 4 a c = 0

b^{2} - 4 a c < 0

The roots of a quadratic equation $a x^{2} + b x + c = 0$ are given by $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , provided $b^{2} - 4 a c \geq 0$ .

Q. Prove the root of equation

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\Rightarrow x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

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