What's the value of b?

Question

The function g is defined by g(x)=2x³-8x²-bx+140. In the xy plane, the graph of g intersects the x-axis at (2,0), (-5,0), and (m,0). What's the value of b?

Answer 1

g(x) = 2x³  - 8x² - bx + 140

 

We know the points (2,0) and (-5,0) are on the graph.

Replace x with 2 and set g(x) = 0 to solve for b

 

2(2³) - 8(2²) - 2b + 140 = 0

16 - 32 - 2b + 140 = 0

124 - 2b = 0

2b = 124

b = 62

 

You can verify by doing the same with x=-5