If `alpha,beta` are zeroes of the polynomial `x^2-2x-15 ,` then form a quadratic polynomial whose zeroes are `(2alpha) and (2beta)dot`

Explanation

alpha And beta be the zero of polynomials comparing equation` x^2 – 2x – 8` comparing ` x^2 – 2x -8` with` x^2 – (alpha + beta)x + 2 beta`

we get `alpha + beta = 2 and alpha beta = -15`

The required quadratic polynomial is `x^2 – 2(alpa beta)x + 4 alpha beta`

`:. 2(alpha + beta) = 2 xx 2 = 4`

And` (2 alpha) (2 beta) = 4 alpha beta = 4 (-15) = - 60`

Putting above values in

`x^2 – 2(alpha + beta)x + 4 alpha beta we get x^2 – 4x – 60`

hence required quadratic polynomial is` x^2 – 4x – 60`