Question

Q.6. The values of p and q if (x+2) is a factor of f(x) =x3 + px2 + qx+6 and f(1) =24 are a) p = 3, q =5 b) p = 6, q = 11 c) p = 5, q =6 d) p = -2, q =7​

Answer 1

Answer:

p = 6, q = 11

Step-by-step explanation:

f(x) = x3 + px2 + qx+6

$({x}^{ 3} + p {x}^{2} + qx + 6) \div x + 2$

f(1) = 24

f(1) = 1^3 + p×1^2 + q×1+6=24

= 1+p+q+6=24

= p+q=17------------eq1

if x+2 is a factor of f(x) = x3 + px2 + qx+6

then remainder = 0 and we can substitute x = -2

by substituting x=-2

we get (-2)^3+p×(-2)^2+q×2+6 = 0

=-8+4p+2q+6=0

=2p+q=1---------------eq2

solving equation 1 and 2 we get p=6,q=11

Answer 2

Step-by-step explanation:

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