Given: x2 + 5x + 6 = 0. On splitting the middle term 5x as 3x + 2x, we get: x2 + 3x + 2x + 6 = 0 = gt; x(x + 3) + 2(x + 3) = 0 = gt; (x + 3) (x + 2) = 0 We ...

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Standard X

Mathematics

Solving a Quadratic Equation by Factorization Method

x2+5 x+6=0

Question

x² + 5x + 6 = 0.

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Solution

Given: x² + 5x + 6 = 0.
On splitting the middle term 5x as 3x + 2x, we get:
x² + 3x + 2x + 6 = 0
=> x(x + 3) + 2(x + 3) = 0
=> (x + 3) (x + 2) = 0
We know that if the product of two numbers is zero, then at least one of them must be zero.
Thus,
x + 3 = 0 or x + 2 = 0
=> x = –3 or x = –2
Therefore, the solution of the given equation is x = –3, –2.

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