College Algebra word problem

Question

If f(x) = ax^ ² − 13x − 7 has the roots -1/2 and 7, find the value of a

Answer 1

f(7) = 0

49a - 91-7 = 0

49a - 98 = 0

49a = 98

a=2

f(x) = 2x^2-13x-7

f(-1/2) = 1/2 +13/2 - 7 = 7-7=0

so yes, f(x) = 2x^2-13x-7