Question

if alpha , beta and gamma are zeroes of a cubic polynomial then the polynomial is _______.

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Answer 1

Answer:

Zeroes of a polynomial means its roots

So let α,β,γ be the roots of a cubic polynomial

We can express the polynomial in two forms

1.From the roots we can write a polynomial as

( x- α)(x- β)(x- γ )=0

2.From knowledge of relation between coefficient and roots .

Let the polynomial be ax³+bx²+cx+d = 0

We know

Σα = α+β+γ = -b/a ;

Σαβ= αβ+βγ+αγ=c/a;

Σαβγ =αβγ =-d/a.

So the above polynomial is written as

x³+b/ax²+c/ax+d/a = 0

x³- (α+β+γ)x² +(αβ+βγ+αγ)x - (αβγ) =0

That's it. Even the first one on expansion will give the same result as second one .

This is the way to represent a polynomial,whose roots are known.

Step-by-step explanation:

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