Find a polynomial fx with leading coefficient 1 such that th

Find a polynomial f(x) with leading coefficient 1 such that the equation f(x) = 0 has the given roots and no others. Express f(x) in the form a_n x^n + a_n - 1^x^n - 1 + ... + a_1^x + a_0. f(x) = x^3 + 5x^2 - 13x - 7 f(x) = x^3 + 13x^2 - 5x + 7 f(x) = x^3 + 5x^2 - 13x + 7 f(x) = x^3 + 5x^2 + 12x + 7 f(x) = x^3 - 5x^2 - 11x + 7

Solution

Lets took the roots first it could be 1,1,-7

f(x) = (x-1)(x-1)(x+7)

f(x) = (x² + 1 - 2x)(x + 7)

f(x) = x³ + 7x² + 1x + 7 - 2x² -14x

f(x) = x³ + 5x² -13x +7

This equation is equal to the option 3rd