Question

If $x^2-hx-21=0,x^2-3hx+35=0(h>0)$ have a common root, then the value of h is equal to

• A. 1
• B. 4
• C. 3
• D. 2

Answer 1

The correct option is B

4

Given, equations $x^2-hx-21=0$ and $x^2-3hx+35=0$ have one root in common.
Let the common root be $\alpha .$
$\Rightarrow {\alpha }^2-h\alpha -21=0$ $.....\left(1\right)$
$\Rightarrow {\alpha }^2-3h\alpha +35=0$ $.....\left(2\right)$
applying condition of one common root we get
$(-21-35{)}^2=(-35h-63h\left)\right(-3h+h)$
$\Rightarrow (-56{)}^2=(-98h\left)\right(-2h)$
$\Rightarrow 3136=196h^2$
$\Rightarrow 16=h^2$
$\Rightarrow \pm 4=h$
$\because h>0$
Hence, $h=4$ is correct.