Question

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

Answer 1

Answer:

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

−81

=−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

Answer 2

Given : The quadratic polynomial p(x) with –24 and 4 as a product and one of the zeros respectively

To Find : Polynomial

Solution:

Product of zeroes =  -24

One zero = 4

Hence other zero = -24/4  = - 6

p(x) = ( x - a)(x - b)

where a nd b are zeroes

p(x) = (x -4)(x - (-6))

= ( x - 4)(x + 6)

= x² + 2x  - 24

p(x) = x² + 2x  - 24

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