Question

Write an quadratic polynomial sum of whose zeroes is 2 and product is -8

Answer 1

Answer:

x2-2x-8

Step-by-step explanation:

product = -8

sum = 2

Answer 2

Step-by-step explanation:

Given,

Sum of zeroes = 2

Product = -8

Let the zeroes be: x, y

Product = xy = -8 - (1)

Sum = x+y = 2

        = y = 2-x - (2)

Substitute Equation (2) in (1)

$xy = -8\\x(2-x) = -8\\2x-x^{2} = -8\\x^{2} -2x-8=0\\x^{2} -4x+2x-8=0\\x(x-4)+2(x-4)=0\\(x-4)(x+2)=0\\x=+4,,-2$

Therefore,   $x^{2} -2x-8=0 \:\:\:is \:\:\:the \:\:\:required\:\:\:polynomial$