unkown77
02.11.2019 •
Mathematics
Apolynomial with integer coefficients is of the form \[x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 18.\]you are told that the integer $r$ is a double root of this polynomial. (in other words, the polynomial is divisible by $(x - r)^2.$) enter all the possible values of $r,$ separated by commas.
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Ответ:
-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
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
Ответ:
you do not need a variable when multiplying fractions and mixed numbers
Step-by-step explanation: