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KCET2007MathematicsDeterminants

The value of | array lll x & p & q p & x & q p & q & x array | is

Options

  1. Ax(x-p)(x-q)
  2. B(x-p)(x-q)(x+p+q)
  3. C(p-q)(x-q)(x-p)
  4. Dp q(x-p)(x-q)

Correct answer

B. (x-p)(x-q)(x+p+q)

Step-by-step solution

Given aligned & | array lll x & p & q p & x & q p & q & x array | =& x [x²-q² ]-p[p x-p q]+q[p q-p x] =& x³-x q²-p² x+p² q+p q²-p q x =& x(x-q)(x+q)-p²(x-q)-p q(x-q) =&(x-q) [x²+x q-p²-p q ] =&(x-q)(x-p)(x+p+q) aligned

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