Question

If $p\left(x\right)=\sqrt{x^2-4x+3}+\sqrt{x^2-9}-\sqrt{4x^2-14x+6}$ then p(3) is

• A. 0
• B. 4
• C. 3
• D. 5

Answer 1

The correct option is A 0

Given, $p\left(x\right)=\sqrt{x^2-4x+3}+\sqrt{x^2-9}-\sqrt{4x^2-14x+6}$
If $3$ is a zero of $p\left(x\right)$, then
$p\left(3\right)=0$
$=>\sqrt{3^2-4\left(3\right)+3}+\sqrt{3^2-9}-\sqrt{4(3{)}^2-14(3)+6}=0$
$=>\sqrt{9-12+3}+\sqrt{9-9}-\sqrt{36-42+6}=0$
$=>\sqrt{12-12}+\sqrt{9-9}-\sqrt{42-42}=0$
$=>0=0$
Thus, $3$ is a zero of $p\left(x\right)=\sqrt{x^2-4x+3}+\sqrt{x^2-9}-\sqrt{4x^2-14x+6}$