3r4 6r3 7r130 How many negative roots can the equation have

-3r⁴ + 6r³ +7r-13=0

How many negative roots can the equation have?

A.2 or 0

B.4 or 2

C.0

D.3 or 1

E.4, 2, or 0

How many imaginary roots can the equation have?

A.4 or 2

B.0

C.4, 2 or 0

D.2 or 0

E.3 or 1

How many positive roots can the equation have?

A.3 or 1

B.2 or 0

C.4, 2, or 0

D.4 or 2

E.0

Solution

f(r) = -3r⁴ + 6r³ +7r-13

Number of sign changes between consecutive terms : 2

No. of positive roots equation can have is 0 or 2

No. of imaginary roots equation can have : 0 or 2

f(-r) = -3r^4 - 6r^3 - 7r -13

Number of sign changes between consecutive terms : 0

No. of negative roots equation can have : 0

So, Q1 : Option C

Q2 : Option D

Q3 : Option B