Answer:-2 and 2
Step-by-step explanation:
Since the polynomial given [x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 18.\] is divisible by (x - r)^2, this means that (x - r)^2 is a factor of the polynomial just like 4 is divisible by 2, we say 2 is a factor.
Since (x - r)^2 is a factor, we equate the factor to zero in order to get the 'x' variable.
(x - r)^2 =0
Taking square root of both sides gives x-r =0 i.e x=r
Substituting x=r into the polynomial to get 'r' we have r^4 + a_3 r^3 + a_2 r^2 + a_1r + 18=0.
Let a be 1 since the coefficients are integers
We then have Answer:
Step-by-step explanation:
Since the polynomial given [x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 18.\] is divisible by (x - r)^2, this means that (x - r)^2 is a factor of the polynomial just like 4 is divisible by 2, we say 2 is a factor.
Since (x - r)^2 is a factor, we equate the factor to zero in order to get the 'x' variable.
(x - r)^2 =0
Taking square root of both sides gives x-r =0 i.e x=r
Substituting x=r into the polynomial to get 'r' we have r^4 + r^3 + r^2 + r + 18=0.
Factorizing this, possible value of r will be -2 and 2
