Carcass wrote:
If -1/2 and -2 are the two roots of the quadratic equation ax2+5x+b=0, then what is the value of a and b?
A. a = -2 and b = -2
B. a = -2 and b = -1
C. a = -2 and b = 1
D. a = 2 and b = 1
E. a = 2 and b = 2
Key concept: If x=−1/2 and x=−2 are roots of the equation, then those values SATISFY the equation.Let's plug
x=−0.5 and
x=−2 into the equation...
If
x=−0.5, we get:
a(−0.5)2+5(−0.5)+b=0Simplify:
0.25a−2.5+b=0Take this prettier, let's multiply both sides by
4 to get:
a−10+4b=0Add
10 to both sides:
a+4b=10If
x=−2, we get:
a(−2)2+5(−2)+b=0Simplify:
4a−10+b=0Add
10 to both sides:
4a+b=10We now have the following system of equations:
a+4b=104a+b=10Solve to get:
a=2 and
b=2Answer: E