Question 1(i)
Check whether the following are quadratic equations:
$(i) (x + 1)^{2} = 2 (x - 3)$

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Solution

$(i) (x + 1)^{2} = 2 (x - 3) \Rightarrow x^{2} + 2 x + 1 = 2 x - 6 \Rightarrow x^{2} + 7 = 0$
It is of the form $a x^{2} + b x + c = 0$ where $a = 1, b = 0, c = 7$ in this case.
Hence, the given equation is a quadratic equation.

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{(x + 1)}^{2} = 2 (x - 3)

(x + 1)^{2} = 2 (x - 3)

Question 1(ii)
Check whether the following are quadratic equations:
$(i i) x^{2} - 2 x = (- 2) (3 - x)$

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

(x + 1)^{2} = 2 (x - 3)

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