Question

If the equations $x^2-11x+a=0$ and $x^2-14x+2a=0$ have a common root, then $a=$

• A. $0,18$
• B. $0,30$
• C. $18,30$
• D. $0,24$

Answer 1

Answer: (D)

$0,24$

$\Rightarrow \frac{{\alpha }^2}{b_1{c}_2-b_2{c}_1}=\frac{\alpha }{c_1{a}_2-c_2{a}_1}=\frac{1}{a_1{b}_2-a_2{b}_1}$
With $\alpha$ being common root
$\Rightarrow \frac{{\alpha }^2}{-11\left(2a\right)-(-14)\left(a\right)}=\frac{\alpha }{a\left(1\right)-2a\left(1\right)}=\frac{1}{1(-14)-1(-11)}$
$\Rightarrow \frac{{\alpha }^2}{-8a}=\frac{\alpha }{-a}=\frac{1}{-3}$
${\alpha }^2=(\frac{a}{3}{)}^2=\frac{8a}{3}$
$\frac{a^2}{3}=8a\Rightarrow a^2=24a$
$a=0,24$