Question

Select the two values of x that are roots of this equation.

2x2 + 7 x + 6 = 0
O A. X=-3
B. X= -4
C. x= -2
D. x= - 3/2

just for those that cant find it!
answer is in the picture, hope that helps

Answer 1

`\implies x = (-2) \qquad or\qquad x = (-3)/(2)`

Explanation:

Given :-

• A quadratic equation is given to us.
• The equation is 2x² + 7x +6=0

And we need to find out the roots of the given equation. We can use the middle term splitting method to find out the roots as ,

Given equation :-

`\implies 2x^2 + 7x +6=0`

Step 1: Find out the factors of 12 :-

We will choose the two factors such that their sum equals to the coefficient of x i.e. 7 .The factors are , 1×12 , 2×6 , 3×4 .

• And 3 + 4 = 7. So we will break the middle term into 3x and 4x .

Step 2 : Breaking the middle term :-

`\implies 2x^2 + 3x+4x +6=0`

Step 3: Take out common from terms :-

`\implies x(2x + 3) +2(2x +3)=0`

`\implies ( x +2)(2x+3)=0`

Step 4 : Equate them with 0 :-

`\implies x = (-2) \qquad or\qquad x = (-3)/(2)`

Hence the correct options are C and D .