Question

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

Answer 1

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.

Answer 2

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.