Question

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





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Answer 1

Product of zeroes = -24

One Of its zeroes = 4

Let the zeroes of quadratic polynomial be α & β

Let β = 4 and given αβ = -24 ==> α = -24/ 4 = - 6

So , the other zero of polynomial is - 6

The Sum of zeroes of polynomial = - 6 + 4 = - 2

x² −(sum of the zeroes of the polynomial)x+(product of the zeroes)

p ( x ) = x² - ( - 2 ) x + ( - 24 )

p ( x ) = x² + 2x - 24

The Quadratic polynomial p ( x ) is x² + 2x - 24

I Hope this helps U

Answer 2

Given:

The product of zeroes of the quadratic polynomial p(x) is -24.

One of the zeroes is 4.

To find:

The quadratic polynomial p(x).

Solution:

A quadratic equation p(x) is given by

${x}^{2} - (sum \: of \: the \: zeroes)x + (product \: of \: the \: zeroes) = 0$

So, first of all, we need to find out the sum of the zeroes.

Let the two zeroes of the polynomial be alpha and beta.

As given,

$\beta = 4$

and

$\alpha \times \beta = - 24$

$\alpha \times 4 = - 24$

$\alpha = - 6$

Sum of the zeroes:

$\alpha + \beta = - 6 + 4 = - 2$

Hence, the quadratic polynomial p(x) is-

${x}^{2} - ( - 2)x + ( - 24) = 0$

${x}^{2} + 2x - 24 = 0$

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

${x}^{2} + 2x - 24 = 0$