Question

If alpha and beta are zeroes of polynomial such that alpha+beta=6 and alpha ×beta =6 then write the polynomial

Answer 1

$\alpha + \beta = 6 \\ \\ \\ \alpha \beta= 6$

Now,.

We know the general expression of Polynomial is as follows :-

$\boxed{ k({x}^{2} - (sum \: of \: zeroes)x + product)}$

Now,

We have :-

$\boxed{sum = 6} \\ \\ \boxed{product = 6}$

So,

The polynomial p(x) can be :-

$\sf{p(x) = k( {x}^{2} - 6x + 6)}$

Now,

We can put any value for k and can obtain as many number of polynomials we want!

So,

The polynomial can be :-

When k = 1

$\bold{p(x) = ({x}^{2} - 6x + 6)}$

Answer 2

Solution :-

Given :-

Alpha & Beta are the Zeroes of the Polynomial.

&

$\alpha + \beta = 6$

&

$\alpha \times \beta = 6$

By Quadratic Formula,

$x² - ( \alpha + \beta)x + ( \alpha * \beta)$

We get,

x² - 6x + 6.

Hence,

The Polynomial Equation is x² - 6x + 6.