Question

Solve the following quadratic equation using the zero product properly8(6 - x)(x+5) 0The solution set is {(Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each solution only once.)

Answer 1

1) 8(6 - x)(x+5)=0 any quadratic equation can be written in this form

a(x-x_1)(x-x_2)=0

The zero product property states that two factors either the first one or the second factor is equal to zero.

a .b =0 a=(6-x) and b =(x+5)

8(6 - x)(x+5)=0

a b

So,

(6-x) =0

x=6

(x+5)=0

x=-5

Then S ={-5,6}

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Alternatively, we can prove that zero product property validity, by solving it traditionally:

Let's expand those parentheses:

8(6 - x)(x+5)=0

8(6x+30-x²-5x)=0

8(-x²-x+30)=0

-8x²-8x+240=0

-8x²-8x+240=0 Divide by -8

x² +x -30=0

Which two numbers whose sum is 1 and their product is -30?

S = _6 + -5 = 1

P = 6 x -5 = -30

Let's swap the sign

S ={-5,6}