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If one of the zeros of a quadratic polynomial of the form x^2

Question

If one of the zeros of a quadratic polynomial of the form $x^{2} + a x + b$ is the negative of the other, then it

has no linear term and the constant term is negative

has no linear term and the constant term is positive

can have a linear term but the constant term is negative

can have a linear term but the constant term is positive

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If one of the zeros of a quadratic polynomial of the form

x^{2} + a x + b

is the negative of the other, then it

8 mins ago

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8 mins ago

Text solutionVerified

We know that equation $a x^{2} + b x + c = 0$

Then sum of roots $= \frac{- b}{a}$ and product of roots $= \frac{c}{a}$

Given quadratic polynomial is,

p (x) = x^{2} + a x + b

Let one of the zero of the polynomial is

α

then the other zero will be

- α

.
Sum of zeros=

α + (- α) = \frac{- a}{1}

0 = \frac{- a}{1}

a = 0

and product of the zeros =

α (- α) = \frac{b}{1}

- α^{2} = b

b = - α^{2}

b

has to be negative.
Hence, option

A

is correct.

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Question Text	If one of the zeros of a quadratic polynomial of the form $x^{2} + a x + b$ is the negative of the other, then it
Answer Type	Text solution:1
Upvotes	150