Question

Select the correct alternative and write it.        

What is the solution of the quadratic equation ` 2x^2-7x+6=0`

विकल्प

• (A) `-3/2,2`

• (B)` 3/2,2`

• (C) `-2,3/2`

• (d)` 2,2/3`

Answer 1

`3/2,2`

Explanation :

` 2x^2-7x+6=0` 

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

In this technique, if we have to factorise an expression like ax² + bx + c , we need to think of 2 numbers such that:

N₁ . N₂ = a × c  =  2 × 6 = 12

And

N₁ +  N₂ = b = -7

After trying out a few numbers we get

N₁ = -3 and N₂ = -4

-3 × -4 = 12  and 

-3 + (- 4) = -7

` 2x^2-7x+6=0`  

`2x^2 - 4x - 3x + 6`

2x (x - 2) - 3 (x - 2) = 0

(2x - 3)(x - 2) = 0

Now we equate the factors to zero and obtain solutions.

2x - 3 = 0 , x = `3/2`

x - 2 = 0  , x = 2

Hence x = `3/2` and x = 2