If (x3 + ax2 + bx +6) has (x - 2) as a factor and leaves a remainder 3 when
divided by (x - 3), find the values of a and b.
Answers
Answer:
Step-by-step explanation:
x^3 + ax^2 +bx + 6
if x-2 is a factor
then x=2
now putting the value of x in eq 1
2^3 + 2^2a +2b +6
4a + 2b + 14 .......(1)
if x-3 is a factor so x=3
and remainder = 3
3^3 + 3^2a+3b+6 = 3
27+9a+3b+6=3
9a+3b+33=3
9a+3b+30=0 ......(2)
\\now from equation 1 and 2
4a + 2b + 14
9a+3b+30=0
⇒ 2a + b + 7 = 0
3a + b+10 = 0
⇒a = -3
and from eq 1
4a + 2b + 14 =0
4*(-3) + 2b + 14 =0
-12 +2b = -14
2b = -14 + 12
2b = -2
b = -1
Given : x³ + ax² + bx + 6 has (x – 2) as a factor and leaves a remainder 3 when divided by (x – 3)
To Find : values of a and b.
Solution:
x³ + ax² + bx + 6 has (x – 2) as a factor
=>for x = 2 value = 0
=> 2³ + a.2² + b.2 + 6 = 0
=> 8 + 4a + 2b + 6 = 0
=> 4a + 2b = - 14
=> 2a + b = - 7
leaves a remainder 3 when divided by (x – 3)
=> for x = 3 value = 3
=> 3³ + a.3² + b.3 + 6 = 3
=> 27 + 9a + 3b + 6 = 3
=> 9a + 3b = -30
=> 3a + b = -10
3a + b = -10
2a + b = - 7
=> a = - 3
b = - 1
Value of a = - 3
Value of b = -1
Learn More:
on dividing x3-3x2+x+2 by a polynomial g(x),the quotient and ...
brainly.in/question/3135153
Divide 9x^3+3x^2-5x+7 by (3x-1) write the quotient and remainder ...
brainly.in/question/6190809
Divide the polynomial (6x³ + 11x² - 10x - 7) by the binomial (2x + 1 ...
brainly.in/question/4743553