Question

Use the zero product property to find the solutions to the equation

2x2 – x – 15 = x(x + 1).

A. x= -5 or x=3

B. x= -7/2 or x=2

C. x= -3 or x=5

D. x= -5/2 or x=3

Answer 1

hello : 
answer : C)    x= -3 or x=5
because : 
x=-3
2(-3)²-(-3)-15 = -3(-3+1)
18+3-15 =6
21-15 = 6....right 
x=5
2(5)²-5-15 = 5(5+1)
50-20 =30
30=30.....right

Answer 2

Answer: The correct option is C.

Explanation:

The given equation is,

$2x^2-x-15=x(x+1)$

Simplify the above equation.

$2x^2-x-15=x^2+x$

$2x^2-x-15-x^2-x=0$

$x^2-2x-15=0$

Use factoring by grouping method.

$x^2-5x+3x-15=0$

$x(x-5)+3(x-5)=0$

$(x-5)(x+3)=0$

According to zero product property the product of two factors is zero if and only of at least one of them is 0.

Equate each factor equal to 0.

$x-5=0$

$x=5$

$x+3=0$

$x=-3$

Therefore the solution is  x=5 or x=-3 and the option C is correct.