Question

$x^2-4x+k$ is a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

4, 1

Find the value of $k$.

Answer 1

Given that,

Sum of roots $=4$

and Product of roots $=1$

Now, the quadratic equation is given by,
$x^2-$(sum of roots)$x+$(product of the roots)

The quadratic polynomial is $x^2-4x+1$

Comparing above with given polynomial $x^2-4x+k$, we get $k=1$.