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Question

# Question 2 Which of the following is not a quadratic equation? (a) 2(x−1)2=4x2−2x+1 (b) 2x−x2=x2+5 (c) (√2x+√3)2=3x2−5x (d) (x2+2x)2=x4+3+4x3

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Solution

## a) Given that, 2(x−1)2=4x2−2x+1 ⇒2(x2+1−2x)=4x2−2x+1 ⇒2x2+2−4x=4x2−2x+1 ⇒2x2+2x−1=0 Which represents a quadratic equation because it has the quadratic form ax2+bx+c=0,a≠0 b) Given that, 2x−x2=x2+5 ⇒2x2−2x+5=0 Which represents a quadratic equation because it has the quadratic form ax2+bx+c=0, a ≠ 0 c) Given that, (√2x+√3)2=3x2−5x ⇒2x2+2√6x+3=3x2−5x ⇒x2−(5+2√6)x−3=0 Which also represents a quadratic equation because it has the quadratic form ax2+bx+c=0, a ≠ 0 d) Given that, (x2+2x)2=x4+3+4x2 ⇒x4+4x2+4x3=x4+3+4x2 ⇒4x3−3=0 Which does not represent a quadratic equation because it does not have the quadratic form ax2+bx+c=0, a ≠ 0

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