How do I write the quadratic equation whose roots are 4 and

How do I write the quadratic equation whose roots are 4 and -2 and the leading coefficient is 1?

Solution

roots of quadratic equation are 4 and -2

==> Quadratic equation is P(x) = (x - 4)(x - (-2) )

==> P(x) = (x -4)(x +2)

==> P(x) = x(x) + x(2) - 4(x) - 4(2)

==> P(x) = x² + 2x - 4x -8

==> P(x) = x² -2x - 8

Hence quadratic equation is P(x) = x² -2x - 8