Question

If the equations $x^2-11x+a=0$ & $x^2-14x+2a=0$ have a common root, then value of $a$ equals

• A. $0,24$
• B. $0,1$
• C. $3,2$
• D. None of these

Answer 1

The correct option is A $0,24$

$x^2-14x+2a=0$
$x^2-11x+a=0$
Subtracting second equation from first, we get
$x(-14+11)+a=0$
$x(-3)=-a$
$x=\frac{a}{3}$ which is the common root
Substituting, we get
$\frac{a^2}{9}-\frac{11a}{3}+a=0$
$a(\frac{a}{9}-\frac{11}{3}+1)=0$
Hence,
$a=0$ or $\frac{a}{9}-\frac{8}{3}=0$
$a=24$.