Question

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

Answer 1

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

Answer 2

Let a=2,b=-3,c=4
Wkt,
x^3-x^2(a+b+c)-x(ab+bc+ca)+ABC
x^3-3x^2-10x-24