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Mathematics

Which of the following is not a quadratic equation?

  1. (x + 2)2 = 2(x + 3)
  2. x2 + 3x = (-1)(1 - 3x)
  3. (x + 2)(x - 1) = x2 - 2x - 3
  4. x3 - x2 + 2x + 1 = (x + 1)3

Quadratic Equations

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Answer

Option 1:

(x+2)2=2(x+3)⇒x2+4+4x=2x+6⇒x2+4x−2x+4−6=0⇒x2+2x−2=0(x + 2)^2 = 2(x + 3) \\[0.5em] \Rightarrow x^2 + 4 + 4x = 2x + 6 \\[0.5em] \Rightarrow x^2 + 4x - 2x + 4 - 6 = 0 \\[0.5em] \Rightarrow x^2 + 2x - 2 = 0

It is a quadratic equation as highest power of x is 2.

Option 2:

x2+3x=(−1)(1−3x)⇒x2+3x=−1+3x⇒x2+3x−3x+1=0x2+1=0x^2 + 3x = (-1)(1 - 3x) \\[0.5em] \Rightarrow x^2 + 3x = -1 + 3x \\[0.5em] \Rightarrow x^2 + 3x - 3x + 1 = 0 \\[0.5em] x^2 + 1 = 0

It is a quadratic equation as the highest power of x is 2.

Option 3:

(x+2)(x−1)=x2−2x−3⇒x2−x+2x−2=x2−2x−3⇒x2−x2−x+2x+2x−2+3=03x+1=0(x + 2)(x - 1) = x^2 - 2x - 3 \\[0.5em] \Rightarrow x^2 - x + 2x - 2 = x^2 - 2x - 3 \\[0.5em] \Rightarrow x^2 - x^2 - x + 2x + 2x - 2 + 3 = 0 \\[0.5em] 3x + 1 = 0

It is not a quadratic equation as highest power of x is not 2.

Option 4:

x3−x2+2x+1=(x+1)3⇒x3−x2+2x+1=x3+1+3x(x+1)⇒x3−x2+2x+1=x3+1+3x2+3x⇒x3−x3−x2−3x2+2x−3x+1−1=0⇒−4x2−x=04x2+x=0x^3 - x^2 + 2x + 1 = (x + 1)^3 \\[0.5em] \Rightarrow x^3 - x^2 + 2x + 1 = x^3 + 1 + 3x(x + 1) \\[0.5em] \Rightarrow x^3 - x^2 + 2x + 1 = x^3 + 1 + 3x^2 + 3x \\[0.5em] \Rightarrow x^3 - x^3 - x^2 - 3x^2 + 2x - 3x + 1 - 1 = 0 \\[0.5em] \Rightarrow -4x^2 - x = 0 \\[0.5em] 4x^2 + x = 0

It is a quadratic equation as highest power of x is 2.

∴ Option 3 is the correct option.

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