Find the least value of p + q if ( $p^{2}$ - 2p) $x^{2}$ + ( $q^{2}$ + q - 2) x = 0 is an identity.

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Solution

The correct option is D
-1

For it to be an identity, $p^{2}$ - 2p = 0 and $q^{2}$ + q - 2 = 0

p = 2 or 0 and (q + 1)(q - 2) = 0

p = 2 or 0 and q = -1 or q = 2

We get the least value of p + q when p = 0 and q = -1

So the least value of p + q = 0 - 1 = -1

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