Math, asked by genz9854, 4 months ago

If x3 + px2 + qx + 5 has (x – 1) as a factor an leaves a remainder 3 when divided by (x -2), find the values of p and q. ​

Answers

Answered by zarabasit68
0

Answer:

p=1 q=-7

Step-by-step explanation:

f(x)=x³+px²+qx+5

f(1)=1³+p(1²)+q(1)+5

=1+p+q+5

=p+q+6

As x-1 is a factor so

f(1)=0

p+q+6=0. eq(1)

now

f(2)=2³+(2)²p+(2)q+5

=8+4p+2q+5

=4p+2q+13

as f(2)=3

so.

4p+2q+13=3

4p+2q+13-3=0

4p+2q+10=0. eq(2)

from eq1 let

p=-q-6. eq(3)

put in eq2

4(-q-6)+2q+10=0

-4q-24+2q+10=0

-2q-14=0

-2q=14

q=14/-2

q=-7

put in eq3.

p=-(-7)-6

p=+7-6

p=1

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