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Find the common root of the quadratic equation

x2 - 3x+2=0 and 2x2 -5x+2.

x2=x square

2
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x2 - 3x+2=0 and 2x2 -5x+2.

x2=x square

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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.

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

The common root is 2.

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2x² - 5x + 2 = 0