Answer :

Let

Recall that the value of a determinant remains same if we apply the operation R_{i}→ R_{i} + kR_{j} or C_{i}→ C_{i} + kC_{j}.

Applying R_{1}→ R_{1} + R_{2}, we get

Applying R_{1}→ R_{1} + R_{3}, we get

Taking the term (5x + λ) common from R_{1}, we get

Applying C_{2}→ C_{2} – C_{1}, we get

Applying C_{3}→ C_{3} – C_{1}, we get

Expanding the determinant along R_{1}, we have

Δ = (5x + λ)[(1)(λ – x)(λ – x)]

∴ Δ = (5x + λ)(λ – x)^{2}

Thus,

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