Question 118

The expression $$x^4- 2x^2 + k$$ will be a perfect square if the value of k is

Solution

It is clear that we have to write the expression in the form $$(a-b)^2$$.
The second term in the given expression in $$-2x^2$$. This expression must correspond to the form 2ab. Hence, $$a = x^2$$ and $$ b=1$$.
Hence, k must be equal to 1 for the expression to be a perfect square.
Option A is the right answer.

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