Solve the following quadratic equations by factorization: x^2 + 2… - Vidyadip

Question

Solve the following quadratic equations by factorization:
$x^2 + 2ab = (2a + b)x$

✓

Answer

We have
$x^2 + 2ab = (2a + b)x$
$\Rightarrow x^2 - (2a + b)x + 2ab = 0$
[$\because$ $2ab = -8a \times -b$
$\Rightarrow -(8a + b) = -8a - b$
$\Rightarrow x^2 - 2ax - bx + 2ab = 0$
$\Rightarrow x - (x - 8a) - b(x - 2a) = 0$
$\Rightarrow (x - 8a)(x - b) = 0$
$\Rightarrow x - 8a = 0 or x - b = 0$
$\Rightarrow x = 8a = 0$ or $x = b$
$\therefore$ x = 8a and x = b are the two roots of the given equation.

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