Question

The square root of $x^4+6x^3+17x^2+24x+16$ is equal to $x^2+3x+4$.

• A. True
• B. False

Answer 1

The correct option is A True

Let square root of given bi quadratic equation be $x^2+px+q$

We will square the given equation

$\Rightarrow x^4+p^2{x}^2+q^2+2p{x}^3+2pqx+2q{x}^2$

Rewriting the terms ;

$\Rightarrow x^4+x^3\left(2p\right)+x^2(p^2+2q)+x\left(2pq\right)+q^2$

Comparing the above equation with given equation ;

$\Rightarrow q^2=16$

$\Rightarrow q=4$

$\Rightarrow 2pq=24$

$\Rightarrow p=3$

$\therefore p=3$ and $q=4$

$\therefore$ square root $=x^2+3x+4$

Hence, the given statement is true.