Question

42. If alpha and beta zeroes of a quadratic polynomial x²- 5, then the quadratic polynomial whose zeroes are 1+alpha and 1+Beta is​

Answer 1

Answer:

The answer is $x^2-2x-4$

Step-by-step explanation:

Given $\alpha,\beta$ are zeroes of $x^2-5$

$\Rightarrow \alpha+\beta=-\dfrac{b}{a}=-\dfrac{0}{1}=0$ and $\alpha\beta=\dfrac{c}{a}=-5$

Sum of zeroes of required polynomials

            $=1+\alpha+1+\beta=2+(\alpha+\beta)=2+0=2$

And product of zeroes

            $=(1+\alpha)(1+\beta)=a+\alpha+\beta+\alpha\beta=1+0-5=-4$

Thus required polynomial is

            $=x^2-(\text{ sum of zeroes }) x+ {\text{ product of zeroes})\\=x^2-2x-4$