Find the values of a and b so that x4 + x3 + 8x2 +ax + b is divisible by 4x2+ 3x – 2.
Asked by miniprasad | 11th May, 2018, 12:32: PM
According to the question,
Let a1x2 + b1x + c1 be the quotient when x4 + x3 + 8x2 +ax + b is divisible by 4x2 + 3x – 2.
x4 + x3 + 8x2 +ax + b = (4x2 + 3x – 2)(a1x2 + b1x + c1)
After simplifying we get
x4 + x3 + 8x2 +ax + b = 4a1x4 + 4b1x3 + 4c1x2 + 3a1x3 + 3b1x2 + 3c1x - 2a1x2 - 2b1x - 2c1
x4 + x3 + 8x2 +ax + b = 4a1x4 + (4b1 + 3a1)x3 + (4c1 + 3b1 - 2a1)x2 + (3c1 - 2b1) x - 2c1
Comparing coefficients on both sides we get,
4a1 = 4 → a1 = 1
4b1 + 3a1 = 1 → 4b1 + 3 = 1 → b1 = -1/2
Similarly using 4c1 + 3b1 - 2a1 = 8 find c1 we get c1 = 23/8
Put the values of a1, b1, c1 in 3c1 - 2b1 = a and - 2c1 = b to find values of a and b.
a = 3×23/8 - 2×(-1/2)
a = 77/8
- 2c1 = b
b = -2 × (23/8) = -23/4
Answered by Sneha shidid | 11th May, 2018, 03:44: PM
- Find whether 3x+2 is a factor of 3x^4+ 5x^3+ 13x-x^2 + 10
- If two of the zeroes of the polynomial f(x)=x4-4x3-20x2+104x-105 are 3+√2 and 3-√2,then use the division algorithm to find the other zeroes of f(x).
- 2x⁴+x³-14x²-15x-8 divide by x²+3x+2
- Using division algorithm find the quotient and remainder of the following: I) x³-6x²+11x-6 by x²+x+1
- if m and n are divided by 4 then 2 and 3 are respectively the remainders find the remainder when m square + n square is divided by 4
- When a polynomial having degree more than 2 is divided by x-2 the remainder is 1.if it is divided by x-3 then remainder is 3.find the remainder,if it is divided by [x-2][x-3]
- If 3 and -3 are two zeros of the polynomial p(x)=x⁴+x³-11x²-9x+18, then find the remaining two zeros of the polynomial
- if x - root 5 is a factor of the cubic polynomial xcube -3 root 5x square +13x -3 root 5 then find all the zeroes of thee polynomial
- Long division??
- DEAR SIR / MADAM PLEASE FIND ATTACHED QUESTION PAPER, I REQUEST YOU TO PLEASE GIVE SOLUTION TO ALL THE QUESTIONS AS PER THE ATTACHMENT.
Kindly Sign up for a personalised experience
- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions
Verify mobile number
Enter the OTP sent to your number