# Find the common root of the quadratic equation x2 - 3x+2=0 and 2x2 -5x+2. x2=x square

2

2015-10-29T00:20:22+05:30

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X² - 3x + 2 = 0 ------------------(1)
2x² - 5x + 2 = 0 ----------------(2)

Multiply equation (1) by 2, we get
2x² - 6x + 4 = 0 -----------------(3)

subtract equation (3) from (2)
2x² - 5x + 2 = 0
2x² - 6x + 4 = 0
(-)     (+)  (-)
x - 2 = 0
⇒ x = 2

The common root is 2.
2015-10-29T00:21:25+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
x² - 3x + 2 = 0
⇒ x² - 2x - x + 2 = 0
⇒ x(x - 2) -1(x - 2) = 0
⇒ (x - 2)(x - 1) = 0
⇒ x = 2 or 1

2x² - 5x + 2 = 0

⇒ 2x² - 4x - x + 2 = 0
⇒ 2x(x - 2) -1(x - 2) = 0
⇒ (x - 2)(2x - 1) = 0
⇒ x = 2 or 1/2

So, the common root of the given quadratic equations is 2.

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