Question

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

Answer 1

Given that zeroes are = 3 , -2 ,-4

= (x-3), (x+ 2) & (x+ 4)

Now for getting the polynomial,
multiply

(x-3) × (x+2) × (x+4)
=> (x^2 + 2x - 3x -6) × (x+4)
=> (x ^2 - x - 6 ) × (x +4)
=> x^3 + 4x^2 -x^2 - 4x - 6x - 24
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=> {x^3 + 3x^2 - 10x - 24} ........ANS

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Answer 2

The zeroes of the cubic polynomial are 3, -2, -4

Required cubic polynomial
p(x)=x^3-(alpha+beta+gamma) X^2+(alpha beta+ beta gamma + alpha gamma) X-(alpha beta gamma)
p(x)= x^3- 3x^2+(-2)x-(-4)
p(x)=x^3- 3x^2- 2x +4

Hope this helps you :-)