Question

Find a quadratic polynomial the sum and product are -8 and 12 respectively. Hence find the zeros​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

GIVEN :-

Let  alpha and beta be two zeros of the polynomial.

$\alpha+\beta=- 8\\\alpha\beta=12$

TO FIND :-

a. The polynomial

b. Zeros of that polynomial

FORMULA :-

As it has two zeros it should be a quadratic polynomial.

$polynomil = {x}^{2}-(\alpha+\beta )x+(\alpha\beta )$

$zeros\: can \: be \: found \: by \: middle \: term \: factorization. \\\\ the \: coefficient \: of \: x \: should \:be\: split \: in \: such \: a \: way \: that \: its \: sum \: would \: equal \: to \: coefficient \: of \: x \: and \: multiply \: to \: give \: product \: of \: coefficient \: of \: {x}^{2} and \: the \: whole \: number.$

SOLUTION :-

polynomial = x ^2 - ( -8) x+ 12

=> x^2 + 8x + 12      

Now its the polynomial , to get zeros we will middle term factorise it make it equals to zero.

x^2 + 8x + 12 = 0

=>X^2 + 6x + 2x + 12 = 0

=> X( x + 6)  + 2 ( x + 6 ) = 0

=> (x + 6)(x + 2) = 0

=> x + 6 = 0       or       x + 2 = 0

=> x = -6            or         x = -2    

THE TWO ZEROS ARE -2 and -6.