Question

The common root of the equations $x^2-7x+10=0$ and $x^2-10x+16=0$ is:

• A. -2
• B. 2
• C. 3
• D. 5

Answer 1

Answer: (B)

2

Let $\alpha$ be the common root.

$\therefore {\alpha }^2-7\alpha +10=0$ ...(1)

and $\therefore {\alpha }^2-10\alpha +16=0$ ...(2)

Subtracting (2) from (1)

$\therefore ({\alpha }^2-7\alpha +10)-({\alpha }^2-10\alpha +16)=0-0$

$\therefore 3\alpha -6=0$

$\therefore \alpha =2$

So, the answer is option (B)