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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+2
The standard form of a quadratic equation is given by
ax2+bx+c=0,
provided a,b and c are real numbers where a0.

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
2x7=x2+2
x22x+9=0, a quadratic equation.

Lastly, let us consider (x+2)3=4x3.
x3+6x2+12x+8=4x3
2x3+6x2+12x+4=0, a cubic equation as the highest degree of x in the given equation is 3.

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