InterviewSolution
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InterviewSolution
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Find the value of k, if x – 1 is a factor of p(x) in each of the following cases : (i) p(x) = x2 + x + k (ii) p(x) = 2x2 + kx + √2(iii) p(x) = kx2 – √2x + 1 (iv) p(x) = kx2 – 3x + k |
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Answer» (i) p(x) = x2 + x + k g(x) = x – 1 k = ? If x – 1 = 0, then x = 1 p(x) = x2 + x + k p(1) = (1)2 + 1 + k p( 1) = 1 + 1 + k p( 1) = 2 + k If g(x) is a factor, then we have r(x) = 0 ∴ p(1) = 0 2 + k= 0 ∴ k = 0 – 2 k = -2 (ii) p(x) = 2x2 + kx + √2 g(x) = x – 1 k = ? If x – 1 = 0, then x = 1 p(x) = 2x2 + kx + √2 p(1) = 2(1)2 + k(1) + √2 = 2(1) + k(l) + √2 p(1) = 2 + k + √2 If (x – 1) is the factor of p(x), then we have p(1) = 0. ∴ 2 + k + = 0 k = -2 – √2 = 0 (iii) p(x) = kx2 – √2x + 1 g(x) = x – 1 k = ? If x – 1 = 0, then x = 1 p(x) = kx2 – √2x + 1 p(1) = k(1)2– √2(1) + 1 = k( 1) – √2 + 1 p(1) = k - √2 + 1 If (x – 1) is the factor of p(x) then we have p(1) = 0. ∴ p(1) = k – √2 + 1 = 0 ∴ k= √2 – 1 (iv) p(x) = kx2 – 3x + k g(x) = x – 1 k = ? If x – 1 = 0, then x – 1 p(x) = kx2 – 3x + k p(1) = k(1)2 – 3(1) + k = k(1) – 3(1) + k = k – 3 + k p(1) = 2k – 3 If (x – 1) is the factor of p(x), then we have p(1) = 0. |
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