Given that (x-5) and (x+3) are factors of x^4+ax^3-34x^2-76x+b. Determine the values of a and b.
S spr1220 New member Joined Nov 11, 2018 Messages 1 Nov 11, 2018 #1 Given that (x-5) and (x+3) are factors of x^4+ax^3-34x^2-76x+b. Determine the values of a and b.
D Deleted member 4993 Guest Nov 12, 2018 #2 spr1220 said: Given that (x-5) and (x+3) are factors of x^4+ax^3-34x^2-76x+b. Determine the values of a and b. Click to expand... One way to solve this would be to apply rational root theorem. The other method could be to use synthetic division and divide the given polynomial by [(x-5)*(x+3)] and require the remainder to be zero. Please show your work and indicate exactly where you are stuck.
spr1220 said: Given that (x-5) and (x+3) are factors of x^4+ax^3-34x^2-76x+b. Determine the values of a and b. Click to expand... One way to solve this would be to apply rational root theorem. The other method could be to use synthetic division and divide the given polynomial by [(x-5)*(x+3)] and require the remainder to be zero. Please show your work and indicate exactly where you are stuck.
L lookagain Elite Member Joined Aug 22, 2010 Messages 3,250 Nov 12, 2018 #3 spr1220 said: Given that (x-5) and (x+3) are factors of x^4+ax^3-34x^2-76x+b. Determine the values of a and b. Click to expand... (x - 5) is a factor of the polynomial, so the corresponding root is 5. (x + 3) is a factor of the polynomial, so the corresponding root is -3. The substitution of these roots for x make the polynomial equal to zero. Another way is to solve this system of equations: \(\displaystyle (5)^4 + a(5)^3 - 34(5)^2 - 76(5) + b = 0\) \(\displaystyle (-3)^4 + a(-3)^3 - 34(-3)^2 - 76(-3) + b = 0\)
spr1220 said: Given that (x-5) and (x+3) are factors of x^4+ax^3-34x^2-76x+b. Determine the values of a and b. Click to expand... (x - 5) is a factor of the polynomial, so the corresponding root is 5. (x + 3) is a factor of the polynomial, so the corresponding root is -3. The substitution of these roots for x make the polynomial equal to zero. Another way is to solve this system of equations: \(\displaystyle (5)^4 + a(5)^3 - 34(5)^2 - 76(5) + b = 0\) \(\displaystyle (-3)^4 + a(-3)^3 - 34(-3)^2 - 76(-3) + b = 0\)
