Question

Find the value(s) 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. $3,-3$
• B. $4,-4$
• C. $0,3$
• D. none of these

Answer 1

Answer: (B)

$4,-4$

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,

$2\lambda a-56=0$

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

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

Putting this value in equation 1, we get,

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

${\lambda }^2=16$

$\lambda =\pm 4$