Question

The polynomial p(x) = x3 + ax2 + bx- 20 when
divided by x - 5 and x - 3 leaves the remainders
O and -2 respectively. Find the values of a and b.

Answer 1

Answer:

the answers of the given problem are a= -9 and b= 24

Answer 2

Answer:

verified answer:

Step-by-step explanation:

Given,

p(x)=x^3+ax^2+bx

x-5=0 x-3=0

x=5 x=3

solution;

p(5) 5^3+a5^2+b×5-20=0

125+25a+5b-20=0

105+25a+5b=0

Divide by 5 both sides

21+5a+b=0 .......(I)

Now, we put,

p(3) 3^3+a3^2+b×3-20=-2

7+9a+3b=-2

9+9a+3b=0

Divide by 3 both sides

3+3a+b=0 ......(ii)

from (I)-(ii),

3+3a+b=21+5a+b

3a-5a=21-3

-2a=18

a=-9

Put the value of a in eq. (I)

3+3(-9)+b=0

3-27+b=0

-24+b=0

b=24

Hope, it's right