Please solve this: Find the quadratic polynomial, sum of whose zeros is 2 and product is -8. Hence find the zeros of the polynomial.

Dear Student,
let α and β be the zeroes of the required polynomial fx.given,α+β=2 and αβ=-8then,fx=x2-α+βx+αβfx=x2-2x+-8fx=x2-2x-8hence the required polynomial is,fx=0x2-2x-8=0x2-4-2x-8=0x2-4x+2x-8=0xx-4+2x-4=0x-4x+2=0x=4,-2so,the zeroes of fx are 4,-2
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