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Question

# Which of the following equations are quadratic equations?

A
(x2+1)2=x4
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B
(x+1)2=x2
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C
(5x2+2x)(7+5x2)=x2+2
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D
(x+2)3=4x3
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Solution

## The correct options are A (x2+1)2=x4 C (5x2+2x)−(7+5x2)=x2+2The standard form of a quadratic equation is given by ax2+bx+c=0, provided a,b and c are real numbers where a≠0. So, let us simplify the given equations to check if they are quadratic or not. Consider (x2+1)2=x4. ⇒x4+2x2+1=x4 ⇒2x2+1=0, a quadratic equation. Simplifying (x+1)2=x2 ⇒x2+2x+1=x2 ⇒2x+1=0, a linear equation (and hence not a quadratic equation). Simplifying (5x2+2x)−(7+5x2)=x2+2 ⇒2x−7=x2+2 ⇒x2−2x+9=0, a quadratic equation. Lastly, let us consider (x+2)3=4−x3. ⇒x3+6x2+12x+8=4−x3 ⇒2x3+6x2+12x+4=0, a cubic equation as the highest degree of x in the given equation is 3.

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