Question

Form a Quadratic polynomial whose sum of zeros is $4$ and the product of zeros is $8$.

Answer 1

Form the quadratic polynomial using a suitable formula

It is given that, the sum of zeroes $=\left(\alpha +\beta \right)=4$

And, the product of zeroes $=\left(\alpha \beta \right)=8$

Where, $\alpha$ and $\beta$ are the roots of the quadratic polynomial.

Now, as we know, the quadratic polynomial can be expressed using its zeros as follows

${\mathit{x}}^{\mathbf{2}}\mathbf{-}\left(\alpha +\beta \right)\mathit{x}\mathbf{+}\left(\alpha \beta \right)$

$=x^2-\left(4\right)x+\left(8\right)$ $\left[\because \left(\alpha +\beta \right)=4,\alpha \beta =8\right]$

$=x^2-4x+8$

Hence, the required quadratic polynomial is $x^2-4x+8$.