Question

James factored f(x)=5r^2 + 24r – 36 as (5r - 6)6r+6). What are the roots?

Answer 1

The corrected factored form of the quadratic equation f(x) = 5r^2 + 24r - 36 is (5r - 6)(r + 6), leading to roots at r = 1.2 and r = -6.

Step-by-step explanation:

The quadratic equation f(x) = 5r^2 + 24r - 36 has been factored incorrectly by James as (5r - 6)(6r + 6). Since the original equation is a quadratic, we can determine the roots by setting the factored form equal to zero and solving for r.

However, we first need to correct the factoring. The correct factoring of the quadratic equation should be f(x) = (5r - 6)(r + 6). Then, by setting each factor equal to zero, we can find the roots:

• 5r - 6 = 0 → r = 6/5 or r = 1.2
• r + 6 = 0 → r = -6

So the roots of the quadratic equation are r = 1.2 and r = -6.