For what value of k will the equation x^2 - 24x + k=0 have two equal real roots?

Answer 1

You gotta plug this into the quadratic equation

when the discriminate is greater than zero you have 2-real

The discriminant is b^2-4ac

so when b^2-4ac>0 you will have 2-real

it will be an inequality

Answer 2

The quadratic equation will have 2 real roots if b² - 4ac >= 0

or 24² - 4K >= 0 or 576 >= 4K or 144 >= K

That is if K is less than or equal to 144, the quadratic will have 2 real roots. Roots come in pairs so for a quadratic, you either have 2 real roots or 2 complex roots.