Given: 10x2 + 3x ndash; 4 = 0 On splitting the middle term 3x as 8x ndash; 5x, we get: 10x2 + 8x ndash; 5x ndash; 4 = 0 #8658; #160;2x(5x + ...

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Solving a Quadratic Equation by Factorization Method

10 x2+3 x-4=0

Question

10x² + 3x – 4 = 0

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Solution

Given: 10x² + 3x – 4 = 0

On splitting the middle term 3x as 8x – 5x, we get:

10x² + 8x – 5x – 4 = 0

$\Rightarrow$ 2x(5x + 4) – 1(5x + 4) = 0

$\Rightarrow$ (5x + 4) (2x – 1) = 0

We know that if the product of two numbers is zero, then at least one of them must be zero.

Thus,

5x + 4 = 0 or 2x – 1 = 0

$\Rightarrow$ x = – $\frac{4}{5}$ or x = $\frac{1}{2}$
Therefore, the solution of the given equation is x = $- \frac{4}{5}$ , $\frac{1}{2}$ .

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