Determine whether the rational root theorem provides a complete list of all roots for the following polynomial functions. f(x) = 4x^2 − 25 A. No, this polynomia
Mathematics
Buglymonse9l8ish
Question
Determine whether the rational root theorem provides a complete list of all roots for the following polynomial functions.
f(x) = 4x^2 − 25
A. No, this polynomial has complex roots
B. No, this polynomial has irrational roots
C. No, this polynomial has irrational and complex roots
D.Yes.
g(x) = 4x^2 + 25
A. No, this polynomial has complex roots
B. No, this polynomial has irrational roots
C. No, this polynomial has irrational and complex roots
D.Yes.
h(x) = 3x^2 − 25
A. No, this polynomial has complex roots
B. No, this polynomial has irrational roots
C. No, this polynomial has irrational and complex roots
D.Yes.
f(x) = 4x^2 − 25
A. No, this polynomial has complex roots
B. No, this polynomial has irrational roots
C. No, this polynomial has irrational and complex roots
D.Yes.
g(x) = 4x^2 + 25
A. No, this polynomial has complex roots
B. No, this polynomial has irrational roots
C. No, this polynomial has irrational and complex roots
D.Yes.
h(x) = 3x^2 − 25
A. No, this polynomial has complex roots
B. No, this polynomial has irrational roots
C. No, this polynomial has irrational and complex roots
D.Yes.
1 Answer

1. User Answers Nirina7
1)
f(x) = 4x^2 − 25
f(x) = 4x^2 − 25 =0 implies 4x²=25, and x²=25/4, so the possible roots are
x=sqrt(25/4= 5/2 or x= sqrt(25/4)= 5/2
so the answer is D.Yes.
2)
g(x) = 4x^2 + 25=0 implies 4x²= 25 and since i²= 1 (complex number)
we can write 4x²= 25= 25i² so the possible root is x= sqrt(25i²/4)=5i/2 or x= sqrt(25i²/4)=5i/2
the answer is A. No, this polynomial has complex roots
3)
h(x) = 3x^2 − 25=0 implies 3x²=25, x²=25/3 so the possible roots are x= sqrt(25/3)= 5/sqrt3 or x=sqrt(25/3)=5/sqrt3
the answer is B. No, this polynomial has irrational roots