Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively $\frac{1}{4},-1$ ?

Answer 1

Solution: -

given

Sum of zeros $=\frac{1}{4}$

Product of zeros $=-1$

Let the zeros Be $\alpha$ and $\beta$

$\therefore \alpha +\beta =\frac{1}{4}$ $\alpha \beta =-1$

By formula we know the reqd quadratic

equation will be given as

$=x^2-(\alpha +\beta )x+\alpha \beta$

$=x^2-\frac{1}{4}x+(-1)$

$=x^2-\frac{1}{4}x-1$

$\Rightarrow \frac{1}{4}(4x^2-x-4)$ (Ans)