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Question

Which of the following equations are quadratic?

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 option is C (5x2+2x)(7+5x2)=x2+2
The standard form of any quadratic equation is ax2+bx+c=0,
where a, b, c [coefficients] are real numbers and a0 [a is called the leading coefficient].

Option A: (x2+1)2=x4
x4+2x2+1=x4
2x2+1=0; This is a quadratic equation.

Option B: (x+1)2=x2
x2+2x+1=x2
2x+1=0; This is a linear equation.

Option C: (5x2+2x)(7+5x2)=x2+2
2x7=x2+2
x22x+9=0; This is a quadratic equation.

Option D: (x+2)3=4x3
x3+6x2+12x+8=4x3
2x3+6x2+12x+4=0
It's not a quadratic equation, it's a cubic equation as the highest power of x is of degree ‘3’.

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