Question

$m{x}^2+x+1$ is a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

$1,1$

Find the value of ${}^{\prime }{m}^{\prime }$.

Answer 1

Let the quadratic polynomial be $a{x}^2+bx+c$ and the zeroes be $\alpha ,\beta$

Given that,
Then Sum of roots = $\alpha +\beta =\frac{-b}{a}=-1$

and Product of roots = $\alpha \beta =\frac{c}{a}=1$

$\Rightarrow a=1,b=1,c=1$

The required quadratic polynomial is $x^2+x+1$ after putting a,b,c.

Comparing with given polynomial $m{x}^2+x+1$, we get $m=1$.