Fundamental Theorem of Algebra
Trending Questions
Q. Fundamental theorem of algebra states that a polynomial equation of n degree have exactly n roots, either real or imaginary.
- True
- False
Q.
Write the degree of the polynomial:
Q. The total possible no. of roots of the equation 4x7+3x6+2x5+9x4+4x3+x2+9x+9=0 is
Q. If the equation x3−8x2+cx+d=0 ∀ c, d∈R has one complex root and one positive root, then select the correct statement.
- c<0, d>0
- c>0, d<0
- c<0, d<0
- c, d>0
Q. The degree of the polynomial function f(x)=(x−1)2(x+2)2 is 4.
- False
- True
Q. Fundamental theorem of algebra states that a polynomial equation of n degree have exactly n roots, either real or imaginary.
- True
- False
Q. The degree of the polynomial function f(x)=(x−1)2(x+2)2 is 4.
- False
- True
Q. The total possible no. of roots of the equation 4x7+3x6+2x5+9x4+4x3+x2+9x+9=0 is
Q.
Let a, b, c be real numbers a≠ 0. If α is a root of a2x2+bx+c=0, β is a root of a2x2−bx−c=0 and 0<α<β, then the equation a2x2+2bx+2c=0 has a root γ that always satisfies:
γ=α+β2
α<γ<β
γ=α+β2
γ=α
Q.
The highest index of the variable x occurring in the polynomial f(x)=a0xn+a1xn−1+a2xn−2+........an−1x+an is called ___________.
Order of the polynomial
Both of these
degree of the polynomial
None of these
Q.
The highest index of the variable x occurring in the polynomial f(x)=a0xn+a1xn−1+a2xn−2+........an−1x+an is called ___________.
Both of these
degree of the polynomial
Order of the polynomial
None of these
Q. The total possible no. of roots of the equation 4x7+3x6+2x5+9x4+4x3+x2+9x+9=0 is
Q.
Total number of values of x, satisfying (√3+1)2x+(√3−1)2x=23x, is equal to
1
3
2
None
Q. Find the total possible number of roots of the equation 4x7+3x6+2x5+9x4+4x3+x2+9x+9=0
- 0
- 3
- 7
- 4
Q. The sum of all non-integer roots of the equation x5–6x4+11x3–5x2–3x+2=0 is
- -5
- -11
- 3
- 6
Q. The maximum possible number of real roots of equation x5−6x2−4x+5=0 is
- 3
- 4
- 5
- 0
Q. Fundamental theorem of algebra states that a polynomial equation of n degree have exactly n roots, either real or imaginary.
- False
- True
Q. The sum of all non-integer roots of the equation x5–6x4+11x3–5x2–3x+2=0 is
- 6
- 3
- -11
- -5