Question

If $x^2-ax-21=0$ and $x^2-3ax+35=0;a>0$ have a common root, then a is equal to:

• A. 1
• B. 2
• C. 4
• D. 5

Answer 1

The correct option is C 4

Let $\alpha$ be a common root of the two given equations, then ${\alpha }^2-3a\alpha +35=0$ and ${\alpha }^2-a\alpha -21=0$. On substracting we get $-2a\alpha +56=0or\alpha =\frac{28}{a}$.
As $\alpha$ is a root of $x^2-ax-21=0,$
$\therefore (\frac{28}{a}{)}^2-a(\frac{28}{a})-21=0$
Or $a^2=4^{2}ora=\pm 4$
$\therefore a>0,$ we get a = 4