Question

Quadratic polynomial p(x) with-24 & 4 as product of one of the zeros respectively is

1) x^2-2x-24
2) x^2+2x-24
3)x^2+2x+24
4) Can't be determined​

Answer 1

Answer:

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Answer 2

Correct option is

A

x

2

+24x−81

Given: Product of zeroes =−81, and one of the zeroes =3

Let the zeroes of the quadratic polynomial be α,β

Let β=3, and given αβ=−81⟹α=

3

−818

=−27

So, the other zero of the polynomial is −27

Also, the sum of the zeroes of the polynomial =−27+3=−24

So the expression of required polynomial p(x) is given by:

x

2

−(sum of the zeroes of the polynomial)x+(product of the zeroes)

⇒p(x)=x

2

−(−24)x+(−81)

⇒p(x)=x

2

+24x−81

Therefore, the quadratic polynomial p(x) is x

2

+24x−81