Question

For which value of $k$ will the equations $x^2-kx-21=0$ and $x^2-3kx+35=0$ have one common root.

• A. $\pm 1$
• B. $\pm 2$
• C. $\pm 4$
• D. none of these

Answer 1

Answer: (C)

$\pm 4$

Let the common root be $\alpha$

$⟹{\alpha }^2-k\alpha -21=\mathrm{0......}\left(1\right)$

${\alpha }^2-3k\alpha +35=\mathrm{0........}\left(2\right)$

$\left(1\right)-\left(2\right)⟹2k\alpha =56⟹\alpha =\frac{28}{k}$

Substituting $\alpha =\frac{28}{k}$ in $\left(1\right)$

$(\frac{28}{k}{)}^2-28-21=0$

$⟹k=\pm 4$