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If you allow solutions that are complex numbers, then there are always two solutions, although the two solutions may be coincident so as to appear as a single solution. If limited to real solution, then two or none, although again, a coincident pair of solutions will appear as a single solution.
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What is a quadratic polynomial which has no zeros?
A quadratic polynomial must have zeros, though they may be complex numbers.A quadratic polynomial with no real zeros is one whose discriminant b2-4ac is negative. Such a polynomial has no special name.
A second-degree polynomial is a quadratic polynomial?
Yes.
How can you determine whether a polynomial equation has imaginary solutions?
To determine whether a polynomial equation has imaginary solutions, you must first identify what type of equation it is. If it is a quadratic equation, you can use the quadratic formula to solve for the solutions. If the equation is a cubic or higher order polynomial, you can use the Rational Root Theorem to determine if there are any imaginary solutions. The Rational Root Theorem states that if a polynomial equation has rational solutions, they must be a factor of the constant term divided by a factor of the leading coefficient. If there are no rational solutions, then the equation has imaginary solutions. To use the Rational Root Theorem, first list out all the possible rational solutions. Then, plug each possible rational solution into the equation and see if it is a solution. If there are any solutions, then the equation has imaginary solutions. If not, then there are no imaginary solutions.
What type of polynomial is 2x2-6x 4?
A quadratic polynomial.
What type of polynomial is 7x2 - 5x plus 2?
It is a quadratic polynomial.
What is a quadratic polynomial which has no zeros?
A quadratic polynomial must have zeros, though they may be complex numbers.A quadratic polynomial with no real zeros is one whose discriminant b2-4ac is negative. Such a polynomial has no special name.
Is a quadratic polynomial a second-degree polynomial?
Yes.
A second-degree polynomial is a quadratic polynomial?
Yes.
How can you determine whether a polynomial equation has imaginary solutions?
To determine whether a polynomial equation has imaginary solutions, you must first identify what type of equation it is. If it is a quadratic equation, you can use the quadratic formula to solve for the solutions. If the equation is a cubic or higher order polynomial, you can use the Rational Root Theorem to determine if there are any imaginary solutions. The Rational Root Theorem states that if a polynomial equation has rational solutions, they must be a factor of the constant term divided by a factor of the leading coefficient. If there are no rational solutions, then the equation has imaginary solutions. To use the Rational Root Theorem, first list out all the possible rational solutions. Then, plug each possible rational solution into the equation and see if it is a solution. If there are any solutions, then the equation has imaginary solutions. If not, then there are no imaginary solutions.
A quadratic polynomial is a third-degree polynomial?
No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).No. A quadratic polynomial is degree 2 (2 is the highest power); a cubic polynomial is degree 3 (3 is the highest power).
What statement must be true of an equation before you can use the quadratic formula to find the solutions?
The quadratic formula can be used to find the solutions of a quadratic equation - not a linear or cubic, or non-polynomial equation. The quadratic formula will always provide the solutions to a quadratic equation - whether the solutions are rational, real or complex numbers.
Sum and product of the zeros of a quadratic polynomial are -12 and -3 respectively what is the quadratic polynomial?
x2 + 15x +36
What type of polynomial is 2x2-6x 4?
A quadratic polynomial.
If you multiply a linear polynomial by a quadratic one what is the degree of the product polynomial?
It will be a cubic polynomial.
True or false A second-degree polynomial is a quadratic polynomial?
true.
What type of polynomial is 7x2 - 5x plus 2?
It is a quadratic polynomial.
In general how many distinct solutions are there to a quadratic equation?
the maximum number of solutions to a quadratic equation is 2. However, usually there is only 1.
