Question

Find a polynomial equation that has roots of -2 and double root 3

Answer 1

x³ + 2x² -3x +6

Explanation:

We need to find the polynomial whose roots are ,

• -2 , √3 and √3.

Say of we have zeroes as , α , β and γ , then the polynomial is ,

=> p(x) = k[ (x - α ) ( x - β) ( x - γ) ]

• where k is constant. Substituting the respective values , we have ,

=> p(x) = k [ ( x - (-2)) ( x - √3) ( x -√3)]

=> p(x) = k[ (x+2)(x² - 3)]

=> p(x) = k[ x(x² - 3) + 2(x² - 3) ]

=> p(x) = k[ x³ - 3x + 2x² - 6 ]

=> p(x) = k[ x³ + 2x² - 3x - 6 ]

Hence the cubic polynomial is x³ + 2x² - 3x + 6 .