Question

Solve b(x)=16x2−25 to find the zeroes of b(x)

Answer 1

b(x)= (4x)^2-(5)^2

b(x)=(4x-5)(4x+5)

The zeros of b are 5/4 and -5/4

Answer 2

5/4 and -5/4

Explanation:

Solve means change b(x) to 0, factor and use zero product property (write two smaller equations)

This equation is a "difference of two squares" or "difference of perfect squares"

b(x) = 16x^2 - 25

0 = (4x - 5)(4x + 5)

Make two smaller equations.



4x-5=0 and 4x+5=0

Solve both of these separately.

4x - 5 = 0

add 5

4x = 5

divide by 4

x = 5/4 and,



4x + 5 = 0

subtract 5

4x = -5

divide by 4

x = -5/4

"zeros" are solutions are roots, are x-intercepts. These are all pretty commonly interchangeable. (Not exactly, technically for a mathematician) But for a student knowing what to do with a question, for all these:

find zeros

find solutions

find roots

find x-intercepts

Set it equal to 0 and solve.

The zeros are 5/4 and -5/4