Question

If $\alpha,\beta$ are the zeros of a polynomial such that $\alpha+\beta=-6 and\alpha\beta=-4$, then write the polynomial.

Answer 1

SOLUTION :

Given : α  and β are the zeroes of the  polynomial

Given :  α +  β = -6  …………….(1)

αβ = -4 ……………..(2)

Then, the quadratic polynomial is :  

k[x² –(sum of the zeroes)x + (product of the zeroes)]

k[x² –(α + β)x + (α β)]

=k[ x² - (-6) x + (-4)]

[From eq 1 & 2]

= k[ x² + 6x - 4]

[K is any non zero real number]

Hence, the polynomial is f(x) = k[ x² + 6x - 4]

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

$\alpha,\beta$ are the zeros of a polynomial such that $\alpha+\beta=-6 and\alpha\beta=-4$

General equation of polynomial,

x^2 - ( sum of the zeroes) x + product of the zeroes.

=> x^2 - ( - 6 )x + ( - 4 )

=> x^2 + 6x - 4.