Question

find the cubic polynomial whose zeros are 3, ½ and -1 ????​

Answer 1

Given: zeroes of a cubic polynomial 3, 1 2' -1

By factor theorem,

(x − 3)(x - 1/1) (x2 (x + 1) are the factors of the cubic polynomial.

We know that (x + a) (x + b) = x² +(a + b) x + ab

Using the factors (x − 3)(x-1/2)we have

× ² + ( - 3 - 1/2 ) x + 3 / 2

=x2-7/2x-3/2

Again (x + 1) (x²-7/2x+3/2)=x3 - 7x² 2/2+

3x/2 +x² 7/2x + 3/2

x3+2x² - 7x2/2+ 3x - 7x /2+3/2 =

= x³ 5x²/ 2 - 2x +3/2

= 2x³ - - 5x² - 4x + 3 is the required cubic

polynomial.