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Solve the following quadratic equations by factorization:

$x 2 + 2 a b = 2 a + b x$

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An Intiative by Sri Chaitanya

2a, b

a, b

a, 2b

3a, b

answer is A.

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Detailed Solution

Given

: x 2 + 2 a b = (2 a + b) x

Convert the given equation to a linear quadratic form

⇒ x 2 + 2 a b = (2 a + b) x ⇒ x 2 + 2 a b − (2 a + b) x = 0 ⇒ x 2 − (2 a + b) x + 2 a b = 0

⇒ x 2 − 2 a x − b x + 2 a b = 0 ⇒ x (x − 2 a) − b (x + 2 a) = 0 ⇒ (x − 2 a) (x − b) = 0

Either

x - 2 a = 0

x - b = 0

⇒

x = 2 a, b

Thus,

2 a

and

b

are the two roots of the given equation

x 2 + 2 a b = (2 a + b) x

.
So, the correct option is 1.

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