Find the values of p and q such that (x - 1)and (x - 3) are factors of px3 + qx2 + 11x - 6
Answer Details
Since (x - 1), is a factor, when the polynomial is divided by (x - 1), the remainder = zero ∴ (x - 1) = 0 x = 1 Substitute in the polynomial the value x = 1 = p(1)3 + q(1)2 + 11(1) - 6 = 0 p + q + 5 = 0 .....(i) Also since x - 3 is a factor, ∴ x - 3 = 0 x = 3 Substitute p(3)3 + q(3)2 + 11(3) - 6 = 0 27p + 9q = -27 ......(2) Combine eqns. (i) and (ii) Multiply equation (i) by 9 to eliminate q 9p + 9q = -45 Subt. 27p+9q=−27−18p=−18 ∴ p = 1