Question

which of the following is a solution of the equation 2x^+x-6=0 (A) x=2 (B) x= -12 (C) 3/2 (D) x= -3​

Answer 1

Answer: C. 3/2

The solution of the equation 2x^2+x-6 is 3/2.

Explanation:

Given,

$2 {x}^{2} + x - 6 \\ \\ 2 {x}^{2} + 4x - 3x - 6 \\ \\ 2x(x + 2) - 3(x + 2) \\ \\ (2x - 3)(x + 2) \\ \\ x = \frac{3}{2} \: or \: x = - 2$

Therefore the solutions of the polynomial are 3/2 and -2.

Answer 2

Question:

Which of the following is a solution of the equation 2x^2+x-6=0

(A) x=2

(B) x=-12

(C) x=3/2

(D)x=-3

Solution :

$\implies 2 x^2 + x - 6 = 0 \\ \implies 2x^2 + (4 - 3)x - 6 = 0 \\ \implies 2x^2 + 4x - 3x - 6 = 0 \\ \implies 2x(x + 2) - 3(x + 2) = 0 \\ \implies (x + 2)(2x - 3) = 0 \\ \implies x + 2 = 0 \: or \: 2x - 3 = 0 \\ \implies x = 0- 2 \: or \: 2x = 0 + 3 \\ \implies x = - 2 \: or \: 2x = 3 \\ \implies x = - 2 \: or \: x = \frac{3}{2}$

If we have to take only one solution of the type of equation then we choose positive value .

$\boxed {\green{\therefore{Option\:(C)\:\frac{3}{2}\:is\:correct.}}}$