What value of b would result in the function defined by x2 + bx + 40 having zeros at -4 and -10?

Question

Please help me I don't know how to do it

Answer 1

'A zero' means when the curve crosses the x-axis (when y = 0)

We are given that there are zeroes when x = -4 and when x = -10

ax² + bx + c is the parabolic graph equation format. Since we are given x-values, we can plug in either one to solve for b. In our case, a = 1 since the coefficient for x² is an understood 1 and c = 40.

Your equation: x² + bx + 40

Set the equation equal to 0 because we are trying to find b when the function is at a zero (y=0)

x² + bx + 40 = 0

Plug in -4 for x to get (-4)² + b(-4) + 40 = 0

Solve for b:

16 + (-4)b + 40 = 0

56 -4b = 0

-4b = -56

b = 14

Test again when x = -10 and b = 14 to see if it makes the equation = 0

(-10)² + (14)(-10) + 40 = ?

100 - 140 + 40 = ?

100 - 140 + 40 = 0

The b value is 14

Answer 2

(x + 4)(x + 10)

x² + 14x + 40

What is the value of b?