If 5 is a root of x²-3x+k=0

Question

If 5 is a root of x²-3x+k=0

Whats k

And how do I solve

Answer 1

Use the quadratic formula. Since 5 is a root,

5 = [3 ± √(9 - 4k)] / 2

Solve for k.

7 = ±√(9 - 4k)

49 = 9 - 4k

40 = -4k

k = -10

Now test the solution. Is 5 a root of

x² - 3x - 10 = 0 ?

x² - 3x - 10 = (x - 5)(x + 2) = 0

The roots are 5 and -2, so we have a good value for k.