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Question

Find the square root of the polynomial: $$9x^4+12x^3+28x^2+16x+16$$ using division method.


A
x23x+5
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B
x23x+5
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C
x2+3x+5
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D
x2+3x+5
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Solution

The correct option is C $$\left|x^2-3x+5\right|$$
$$\div$$$$x^2-3x+5$$ <= Quotient
$$3x^2$$
$$9x^4+12x^3+28x^2+16x+16$$
$$9x^4$$
$$6x^2+2x$$$$12x^3+28x^2$$
$$12x^3+4x^2$$
$$6x^2+4x+4$$$$24x^2+16x+16$$
$$24x^2+16x+16$$
Remainder $$\Rightarrow 0$$
The square root of $$9x^4+12x^3+28x^2+16x+16$$ is $$\left|x^2-3x+5\right|$$

Mathematics

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