Question

The value(s) of k for which equations $3x^2+4kx+2=0and2x^2+3x-2=0$ will have a common root can be:

• A. $\frac{-11}{8}$
• B. $\frac{11}{8}$
• C. $\frac{7}{4}$
• D. $\frac{-7}{4}$

Answer 1

Answer: (A), (C)

$\frac{7}{4}$

Let $\alpha$ be the common root of both the given equations.
$\therefore 3{\alpha }^2+4k\alpha +2=0and2{\alpha }^2+3\alpha -2=0$
On solving by cross multiplication method we get:
$\frac{{\alpha }^2}{-8k-6}=\frac{-\alpha }{-6-4}=\frac{1}{9-8k}\Rightarrow \alpha =\frac{10}{9-8k}...\left(i\right)and{\alpha }^2=\frac{8k+6}{8k-9}...\left(ii\right)Onsimplifying\left(i\right)and\left(ii\right)weget:32k^2-12k-77=0\Rightarrow 32k^2-56k+44k-77=0\Rightarrow 8k(4k-7)+11(4k-7)=0\Rightarrow (8k+11)(4k-7)=0\Rightarrow k=\frac{-11}{8},\frac{7}{4}$