Question 1 of 11beginner💡 UnderstandShort Answer1 mark

Check whether the following are quadratic equations:

(i)

(x+1)2=2(x−3)(x+1)^2 = 2(x-3)

Answer

Yes, it is a quadratic equation.

(ii)

x2−2x=(−2)(3−x)x^2 - 2x = (-2)(3-x)

Answer

Yes, it is a quadratic equation.

(iii)

(x−2)(x+1)=(x−1)(x+3)(x-2)(x+1) = (x-1)(x+3)

Answer

No, it is not a quadratic equation.

(iv)

(x−3)(2x+1)=x(x+5)(x-3)(2x+1) = x(x+5)

Answer

Yes, it is a quadratic equation.

(v)

(2x−1)(x−3)=(x+5)(x−1)(2x-1)(x-3) = (x+5)(x-1)

Answer

Yes, it is a quadratic equation.

(vi)

x2+3x+1=(x−2)2x^2 + 3x + 1 = (x-2)^2

Answer

No, it is not a quadratic equation.

(vii)

(x+2)3=2x(x2−1)(x+2)^3 = 2x(x^2-1)

Answer

No, it is not a quadratic equation.

(viii)

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

Answer

Yes, it is a quadratic equation.

Explanation

A quadratic equation must be of the form ax² + bx + c = 0, where a ≠\neq 0. We need to simplify each equation to check if it reduces to this standard form. Some equations may appear quadratic initially but simplify to linear equations, while others may appear cubic but simplify to quadratic equations.

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