Question

Find the value of 'a' so that $x^2-11x+a=0and{x}^2-14x+2a=0$ have a common root.

• A. 0
• B. 12
• C. 24
• D. 48

Answer 1

Answer: (A), (C)

The correct options are
A

0

C

24

$x^2-14x+2a=0$

$x^2-11x+a=0$

Let the common root be $\alpha$

$\frac{{\alpha }^2}{-14a+22a}=\frac{-\alpha }{a-2a}=\frac{1}{-11+14}$

$\Rightarrow$$\underset{\left(1\right)}{\frac{{\alpha }^2}{8a}}$ = $\underset{\left(2\right)}{\frac{\alpha }{a}}$ = $\underset{\left(3\right)}{\frac{1}{3}}$

$\alpha =\frac{a}{3}$ $=\frac{8a}{a}$

$\downarrow \downarrow$

From (2), (3) From (1), (2)

$\Rightarrow$ $a^2-24a$ = 0

$\Rightarrow$ a = 0 or 24