Question

Find all real numbers z for which the equation (z-5)x^2-zx+5=0 only has one real solution. If you find more than one, then list the values separated by commas.

Answer 1

Explanation:

For the quadratic equation to have 1 repeated real solution, the discriminant b² - 4ac must be zero.

=> (-z)² - 4(z - 5)(5) = 0

=> z² - 20(z - 5) = 0

=> z² - 20z + 100 = 0

=> (z - 10)² = 0

Therefore z = 10.