Question

Find the values of $\lambda$ so that the equations $x^2-\lambda x-21=0$ and $x^2-3\lambda x+35=0$ may have one common root.

• A. $\pm 1$
• B. $\pm 2$
• C. $\pm 3$
• D. $\pm 4$

Answer 1

The correct option is D $\pm 4$

Let $a$ be the common root of the given equations, then,

$a^2-\lambda a-21=0$ and $a^2-3\lambda a+35=0$.

Subtracting second from the first, we get,

$2\lambda a-56=0$

$2\lambda a=56$

$a=\frac{56}{2\lambda }$

$a=\frac{28}{\lambda }$

Putting this value of $a$ in $a^2-\lambda a-21=0$, we get,

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

$(\frac{28}{\lambda }{)}^2-49=0$

$16-{\lambda }^2=0$

${\lambda }^2=16$

$\lambda =\pm 4$