Question

find a cubic polynomial whose zeroes are 2,-3,4

Answer 1

(x - 2)(x + 3)(x - 4)
(x - 2)(x² - 4x + 3x - 12)
(x - 2)(x² - x - 12)
x³ - x² - 12x - 2x² + 2x + 24
x³ - 3x² - 10x + 24

Answer 2

x³ -(sum of roots )x² + ( sum of products of two roots) x - product of all roots

let a , b and c are the roots of a polynomial so,

a + b + c = 2 -3 + 4 = 3

ab + bc + ca = 2×-3 + -3× 4 + 4× 2

= -6 -12 +8 = -10

abc = 2× -3 × 4 = -24

now,

polynomial is -----

x³-( a + b + c)x² + (ab +bc +ca)x -abc =0

x³ -3x² -10x + 24 = 0

I HOPE U UNDERSTAND