Question

Select the two values of x that are roots of this equation 2x^2 + 7x + 6=0

A. X=-3
B. X=-3/2
C. X=-4
D. X=-2

Answer 1

B and D

Explanation:

Given

2x² + 7x + 6 = 0

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 6 = 12 and sum = + 7

The factors are + 4 and + 3

Use these factors to split the x- term

2x² + 4x + 3x + 6 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) + 3(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x + 3) = 0

Equate each factor to zero and solve for x

x + 2 = 0 → x = - 2 → D

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = -
`(3)/(2)` → B

Answer 2

x = -2 or x = -3/2 thus B. & D. are the answer

Explanation:

Solve for x:

2 x^2 + 7 x + 6 = 0

Hint: | Factor the left hand side.

The left hand side factors into a product with two terms:

(x + 2) (2 x + 3) = 0

Hint: | Find the roots of each term in the product separately.

Split into two equations:

x + 2 = 0 or 2 x + 3 = 0

Hint: | Look at the first equation: Solve for x.

Subtract 2 from both sides:

x = -2 or 2 x + 3 = 0

Hint: | Look at the second equation: Isolate terms with x to the left hand side.

Subtract 3 from both sides:

x = -2 or 2 x = -3

Hint: | Solve for x.

Divide both sides by 2:

Answer: x = -2 or x = -3/2