Question

If the equations $2x^2-7x+9=0$ and $a{x}^2+bx+18=0$ have a common root, then $\left(a,b\in R\right)$

• A. $a=2,b=-7$
• B. $a=\frac{-7}{2},b=1$
• C. $a=4,b=-14$
• D. $a=4,b=-7$

Answer 1

Answer: (C)

$2x^2-7x+9=0$ has complex roots since D $<0$
Complex roots occur in conjugate pair if the coefficients are real.
Hence, if it is given that one root of the equations is common, both roots will be common.
So, the coefficients of the equations will be proportional
$\Rightarrow \frac{2}{a}=\frac{-7}{b}=\frac{9}{18}$
$\Rightarrow a=4$ and $b=-14$