#1
Which of the following is a root of the polynomial equation x^2 - 4 = 0?
#2
What is the degree of the polynomial 3x^4 - 2x^2 + 7?
#3
If the polynomial equation x^3 - 6x^2 + 11x - 6 = 0 has roots a, b, and c, what is the sum of the roots (a + b + c)?
#4
What is the relationship between the roots and coefficients of a quadratic equation ax^2 + bx + c = 0?
Roots are negative of the coefficients
Roots are reciprocals of the coefficients
Roots are squares of the coefficients
Roots are the coefficients themselves
#5
If the polynomial equation 2x^3 - 5x^2 + 3x - 7 = 0 has a root x = 2, what is one factor of the polynomial?
(x - 2)
(2x + 1)
(x + 2)
(2x - 1)
#6
For a quartic polynomial f(x) = x^4 - 6x^3 + 11x^2 - 6x + 1, what is the leading coefficient?
#7
If a quadratic equation ax^2 + bx + c = 0 has no real roots, what can be said about the discriminant (Δ)?
Δ > 0
Δ = 0
Δ < 0
Cannot determine from the given information.
#8
For a cubic polynomial f(x) = x^3 - 3x^2 - 4x + 12, how many real roots does it have?
#9
What is the Rational Root Theorem used for in the context of polynomial equations?
To find irrational roots of the equation
To find all possible rational roots of the equation
To determine the degree of the polynomial
To simplify complex roots
#10
What is the fundamental theorem of algebra in the context of polynomial equations?
Every polynomial equation has at least one real root.
Every polynomial equation can be factored into linear terms.
The degree of a polynomial equation is equal to the number of its real roots.
The sum of the roots of a polynomial equation is equal to the negative of the coefficient of the linear term.
#11
If a polynomial equation has complex conjugate roots, what can be said about the coefficients of the polynomial?
All coefficients are real.
All coefficients are imaginary.
The leading coefficient is imaginary.
The constant term is imaginary.
#12
What is the relationship between the roots and the coefficients of a cubic equation ax^3 + bx^2 + cx + d = 0?
Roots are proportional to the coefficients.
Roots are inversely proportional to the coefficients.
Roots are the negative of the coefficients.
No specific relationship between roots and coefficients.