1.

Check whether the following are quadratic equations:(i) (x – 2)2 + 1 = 2x – 3 (ii) x(x + 1) + 8 = (x + 2) (x – 2)(iii) x (2x + 3) = x2 + 1 (iv) (x + 2)3 = x3 – 4

Answer»

(i) LHS = (x – 2)2 + 1 = x2 – 4x + 4 + 1 = x2 – 4x + 5

Therefore, (x – 2)2 + 1 = 2x – 3 can be rewritten as

x2 – 4x + 5 = 2x – 3

i.e., x2 – 6x + 8 = 0

It is of the form ax2 + bx + c = 0.

Therefore, the given equation is a quadratic equation.

(ii) Since x(x + 1) + 8 = x2 + x + 8 and (x + 2)(x – 2) = x2 – 4

Therefore, x2 + x + 8 = x2 – 4

i.e., x + 12 = 0

It is not of the form ax2 + bx + c = 0.

Therefore, the given equation is not a quadratic equation.

(iii) Here, LHS = x (2x + 3) = 2x2 + 3x

So, x (2x + 3) = x2 + 1 can be rewritten as

2x2 + 3x = x2 + 1

Therefore, we get x2 + 3x – 1 = 0

It is of the form ax2 + bx + c = 0.

So, the given equation is a quadratic equation.

(iv) Here, LHS = (x + 2)3 = x3 + 6x2 + 12x + 8

Therefore, (x + 2)3 = x3 – 4 can be rewritten as

x3 + 6x2 + 12x + 8 = x3 – 4

i.e., 6x2 + 12x + 12 = 0 or, x2 + 2x + 2 = 0

It is of the form ax2 + bx + c = 0.

So, the given equation is a quadratic equation.


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