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Question
Select the correct alternative and write it.
What is the solution of the quadratic equation ` 2x^2-7x+6=0`
Options
(A) `-3/2,2`
(B)` 3/2,2`
(C) `-2,3/2`
(d)` 2,2/3`
Solution
`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
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