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Question

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


A
True
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B
False
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Solution

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 

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

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

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