What are all of the real roots of the following polynomial? f(x) = x4 - 24x2 - 25
2 answers:
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Answer:
Step-by-step explanation:
Given :
Solution :
Part A:
First find the potential roots of p(x) using rational root theorem;
So,
Since constant term = -60
Leading coefficient = 1
Thus the possible roots are
Thus from the given options the correct answers are -10,-5,3,15
Now For Part B we will use synthetic division
Out of the possible roots we will use the root which gives remainder 0 in synthetic division :
Since we can see in the figure With -5 we are getting 0 remainder.
Refer the attached figure
We have completed the table and have obtained the following resulting coefficients: 1 , 1,−12,0. All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
Thus the quotient is
And remainder is 0 .
So to get the other two factors of the given polynomial we will solve the quotient by middle term splitting
Thus x-3 and x+4 are the other two factors
So , p(x)=(x+5)(x-3)(x+4)
Answer:
Table is attached with values, but answers are:
(0, 0) (1, 3) (2, 6) (3, 9)
Step-by-step explanation:
y = 3x
Substitute all values.
y = 3(0)
y = 0
0, 0
y = 3(1)
y = 3
1, 3
y = 3(2)
y = 6
2, 6
y = 3(3)
y = 9
3, 9
