Find the values of p and q such that (x - 1)and (x - 3) a...
Find the values of p and q such that (x - 1)and (x - 3) are factors of px3 + qx2 + 11x - 6
-1, -6
1, -6
1, 6
6, -1
Correct answer is B
Since (x - 1), is a factor, when the polynomial is divided by (x - 1), the remainder = zero
\therefore (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, \therefore 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
Subtract (ii) from (i), 18p = 18
\therefore p = 1
Put p = 1 in (i),
1 + q = -5 \implies q = -6
(p, q) = (1, -6)
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