Question

Solve z^2-2z-35=0 using zero product

Answer 1

Answer: z = 7 or z=-5

Explanation:

First you need to factor the polynomial.

To factor
`z^(2)` - 2z -35 You will need to find two numbers that their product is -35 and their sum is -2 and the numbers -7 and 5 works out.

Rewrite the polynomial as,

`z^(2)` - 7z + 5z - 35 = 0 factor the left by grouping

(
`z^(2)` -7z) (5z -35) = 0

z(z -7) 5(z - 7) = 0 Factor out z-7

(z-7)(z+5) = 0 Now apply the zero product by setting each of them equal 0.

z-7= 0 or z+5=0

+7 +7 -5 -5

z = 7 or z= -5