Question

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

Answer 1

Answer:

$\implies x = (-2) \qquad or\qquad x = \dfrac{-3}{2}$

Step-by-step 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 :-

$\implies x = (-2) \qquad or\qquad x = \dfrac{-3}{2}$

Hence the correct options are C and D .