Which of the following is a quadratic equation? A) (x – 2) (x + 1)

1.	Which of the following is a quadratic equation? A) (x – 2) (x + 1) = (x – 1) (x + 3)B) x4 – 1 = 0 C) (x + 1)2 = 2(x – 3) D) x2 + 3x + 1 = (x – 2)2
Answer» Correct option is (C) (x + 1)² = 2(x – 3) Standard form of quadratic equation is \(ax^2+bx+c=0,a\neq0.\) (A) \((x-2)\,(x+1)=(x-1)\,(x+3)\) \(\Rightarrow x^2-2x+x-2=x^2-x+3x-3\) \(\Rightarrow x^2-x-2=x^2+2x-3\) \(\Rightarrow 2x-3+x+2=0\) \(\Rightarrow3x-1=0\) which is a linear equation. (B) \(x^4-1=0\) which is a quartic equation. (C) \((x+1)^2=2(x-3)\) \(\Rightarrow x^2+2x+1=2x-6\) \(\Rightarrow x^2+2x+1-2x+6=0\) \(\Rightarrow x^2+7=0\) which is a quadratic equation. (D) \(x^2+3x+1=(x-2)^2\) \(\Rightarrow x^2+3x+1=x^2-4x+4\) \(\Rightarrow7x-3=0\) which is a linear equation. Correct option is C) (x + 1)² = 2(x – 3)

Which of the following is a quadratic equation? A) (x – 2) (x + 1) = (x – 1) (x + 3)B) x4 – 1 = 0 C) (x + 1)2 = 2(x – 3) D) x2 + 3x + 1 = (x – 2)2

Answer»

Correct option is (C) (x + 1)² = 2(x – 3)

Standard form of quadratic equation is \(ax^2+bx+c=0,a\neq0.\)

(A) \((x-2)\,(x+1)=(x-1)\,(x+3)\)

\(\Rightarrow x^2-2x+x-2=x^2-x+3x-3\)

\(\Rightarrow x^2-x-2=x^2+2x-3\)

\(\Rightarrow 2x-3+x+2=0\)

\(\Rightarrow3x-1=0\) which is a linear equation.

(B) \(x^4-1=0\) which is a quartic equation.

(C) \((x+1)^2=2(x-3)\)

\(\Rightarrow x^2+2x+1=2x-6\)

\(\Rightarrow x^2+2x+1-2x+6=0\)

\(\Rightarrow x^2+7=0\) which is a quadratic equation.

(D) \(x^2+3x+1=(x-2)^2\)

\(\Rightarrow x^2+3x+1=x^2-4x+4\)

\(\Rightarrow7x-3=0\) which is a linear equation.

Correct option is C) (x + 1)² = 2(x – 3)