Question

write quadratic polynomial whose
sum of zeroes is 2 and product is -8​

Answer 1

Let p(x) be the polynomial

$let \: \alpha \: and \: \beta \: be \: the \: zeroes \: of \: p(x)$

Given,

Sum of zeroes = 2

So,

$\alpha + \beta = 2$

Product of zeroes = -8

So,

$\alpha \beta = - 8$

We know the formula

$p(x) = {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ for \: a \: quadratic \: polynomial$

Substituting the value

$p(x) = {x}^{2} - (2)x + ( - 8) \\ \\ = {x}^{2} - 2x - 8$

Hence, the quadratic polynomial is x²-2x-8

Answer 2

Answer:

let's polynomial be

p(x)= ax²+bx+c

sum of zeros = 2 product of zeros= -8

-b/a = -2/1 c/a = -8/1

assuming a=1 assuming a =1

so, a=1,b=-2,c=-8

ax²+bx+c

put the values

x²+(-2x)+(-8)

x²-2x-8