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The quadratic polynomial $p (x)$ with -24 and 4 as a product and one of the zeros respectively is

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x 2 − 2 x − 24

x 2 + 2 x − 24

x 2 + 2 x + 24

Can't be determined

answer is B.

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Detailed Solution

Given the product and one of the zero of a quadratic polynomial

p (x)

are -24 and 4 respectively.
We have to find the polynomial.
In quadratic equation

a x 2 + b x + c = 0

,
product of roots is

c a

.
Let us consider roots be

α, β

.
According to the question we have

c a = − 24 ⇒ α × β = − 24

And

α = 4

Then

β = − 24 4 β = − 6

So sum of roots

α + β = 4 − 6 α + β = − 2

Therefore, the equation is given as

x 2 − sum of roots x + product of roots

x 2 − − 2 x + − 24

.
Required polynomial is

p (x) = x 2 + 2 x − 24

Hence, the correct answer is 2.

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