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Question

Which of the following equations are quadratic?

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

The correct option is D (5x2+2x)−(7+5x2)=x2+2The standard form of any quadratic equation is ax2+bx+c=0, where a, b, c [coefficients] are real numbers and a≠0 [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 ⇒2x−7=x2+2 ⇒x2−2x+9=0; This is a quadratic equation. Option D: (x+2)3=4−x3 ⇒x3+6x2+12x+8=4−x3 ⇒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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