Question

Find the zeroes of the quadratic polynomial
f(x) = mx(x -m-1) + m2

and verify the relationship
between the zeroes and its coefficients.​

Answer 1

Step-by-step explanation:

$f(x) = m {x}^{2} - m(m - 1)x + {m}^{2} = 0$

dividing the whole equation by m we get

${x}^{2} - (m - 1)x + m = 0$

by quadratic formula

$x = \frac{m - 1 + \sqrt{ {(m - 1)}^{2} - 4m } }{2} \: \: \: and \: \: \frac{m - 1 - \sqrt{ {(m - 1)}^{2} - 4m } }{2}$