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CBSE Class 12 · DeterminantsVery Short Answer

If

f (x) = a a x a x^{2} - 1 a a x 0 - 1 a

, using properties of determinants find the value of

f (2 x) - f (x)

.

Answer: $a x (3 x + 2 a)$

Solution

Expanding (or simplifying with column operations), the determinant works out to

f (x) = a (a^{2} + 2 a x + x^{2}) = a (a + x)^{2} .

Then

f (2 x) = a (a + 2 x)^{2} = a (a^{2} + 4 a x + 4 x^{2})

and

f (x) = a (a^{2} + 2 a x + x^{2})

, so

f (2 x) - f (x) = a [(4 x^{2} + 4 a x) - (x^{2} + 2 a x)] = a (3 x^{2} + 2 a x) = a x (3 x + 2 a) .

a x (3 x + 2 a)

CBSE Class 12 Board · Subjective

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