Question

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

A
True
B
False

Solution

## The correct option is A TrueLet square root of given bi quadratic equation be $$x^{2}+px+q$$We will square the given equation $$\Rightarrow x^{4}+p^{2}x^{2}+q^{2}+2px^{3}+2pqx+2qx^{2}$$Rewriting the terms ;$$\Rightarrow x^{4}+x^{3}(2p)+x^{2}(p^{2}+2q)+x(2pq)+q^{2}$$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.Maths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More