Question

Given that quadratic equation $a{x}^2+bx+c=0$ where $a,b,c\in Q$ has an irrational root and the other root is common with a root of quadratic equation$d{x}^2+ex+f=0$ for $d,e,f\in Q.$ Then the value of $\frac{a^{2}ef}{d^{2}bc}$ is

• A. $\frac{3}{2}$
• B. $\frac{1}{2}$
• C. Any real number
• D. $1$

Answer 1

The correct option is D $1$

Since coefficients are rationals, irrational root occurs in conjugate pair.
Both the roots of both quadratic equation will be same, hence
$\frac{a}{d}=\frac{b}{e}=\frac{c}{f}$
$\therefore \frac{a^{2}ef}{d^{2}bc}=1$