Post a New Question

math

posted by .

if x3+ax2-bx+10 is divisible by x2-3x+2 .find the value of a and b

  • math -

    since x^2 - 3x + 2 = (x-2)(x-1)
    so x^3 + ax^2 -bx + 10 must be divisible by both
    x-2 and x-1

    let f(x) = x^3 + ax^2- bx + 10
    f(2) = 5 + 4a - 2b + 10 = 0 ---> 4a - 2b = -15
    f(1) = 1 + a - b + 10 ---> a-b = -11 or a = b-11

    sub 2nd into 1st
    4(b-11) - 2b = -15
    4b - 44 - 2b = -15
    2b = 29
    b = 29/2
    then a = 29/2 - 11 = 7/2

  • math -

    good

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    I'm having some troubles with these. Thanks in advance. If a>0 find the minimum value. If a<0 find the maximum value. 1. y=-x²+2x+5 2. y=-2x²-3x+4 These are functions for parabolas, so f(x)=ax²+bx+c when a does not equal 0 …
  2. Math

    The question is this: You know that a number is divisible by 6 if it is divisible by both 3 and 2. So why isn't a number divisible by 8 if it is divisible by both 4 and 2?
  3. math

    is 504 divisible by 2,4,6,8 is 111 divisible by 3,9 is 3,217 divisible by 3 is 804 divisible by 2,4,6,8
  4. math

    find a such that f(x)= ax2-4x+3 has a maximum value of 12
  5. math

    find a such that f(x)= ax2-4x+3 has a maximum value of 12
  6. math

    Find the value of the missing digit that makes the statement true. 214,21_ is divisible by 11 Determine whether the statement is true or false. Why?
  7. math

    Using the numbers 1 through 9 with no repeats, find a 9 number such that: the first digit is divisible by 1, the first two digits are divisible by 2, the first 3 digits are divisible by 3, and so on until we get to a 9 digit number …
  8. Math PLEASE HELP!!!

    Which of the following is false? a. A number that is divisible by 3 and 20 is divisible by 60. b. A number that is divisible by 4 and 15 is divisible by 60. c. A number that is divisible by 5 and 12 is divisible by 60. d. A number
  9. precalculus

    can you please check my work? 7. Find the equation of the parabola y=ax2+bx+c that passes through the points(0,6),(-2,2), and(3,9/2). y=ax2+bx+c 6=a(0)2+b(0)+c 2=a(-2)2+b(-2)+c 9/2=a(3)2+b(3)+c 6=c 2=4a+(-2b)+6 9/2=9a+3b+6 -4=4a-2b
  10. number theory

    The values A,B,C, and [(A/B)+C], are all integers which are divisible by 3. Then, which of the following statements must be true: A is divisible by 9 B is divisible by 9 C is divisible by 9 A and B are both divisible by 9 A,B,and C …

More Similar Questions

Post a New Question