Question

If $\alpha and\beta$ are the zeros of the quadratic polynomial $f\left(x\right)=x^2-1$, find a quadratic polynomial whose zeros are $\frac{2\alpha }{\beta }and\frac{2\beta }{\alpha }$

Answer 1

Given the polynomial,

and the roots of the polynomial are .
Hence the sum of zeros = -b/a
And product of zeros = c/a
Here, a=1, b=0 and c=-1.



Now, If the zeros of the polynomial are

So, the sum of zeros= -4
Again, the product of the zeroes

Now the required quadratic equation is;

$K(x^2-(sumofzeroes)x+(productofzeroes)$

$K(x^2+4x+4)=0$