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How to tell if there are no real roots?
The real roots of what, exactly? If you mean a square trinomial, then: If the discriminant is positive, the polynomial has two real roots. If the discriminant is zero, the polynomial has one (double) real root. If the discriminant is negative, the polynomial has two complex roots (and of course no real roots). The discriminant is the term under the square root in the quadratic equation, in other words, b2 - 4ac.
What is the polynomial having two terms?
A polynomial with two terms is called a binomial.
What are the different forms in quadratic equation?
The general form of a quadratic equation is y = ax2 + bx + c, where a, b and c are real constants and a ≠0. If a = 0 then it is not a quadratic! There are two ways of classifying the forms. "CUP OR CAP" If a > 0 then the graph of the quadratic is cup shaped - like a U. If a < 0 then the graph is cap shaped - like an inverted U. "NUMBER OF ROOTS" Using the above form, calculate the discriminant, d = b2 - 4ac If d > 0 the quadratic has two real roots. That is, two distinct real values of x for which y = 0. If d = 0 the quadratic has two coincident real roots. (Some consider this as one root but it is useful to consider the situation as two roots that coincide since that approach maintains parity between the number of roots and the order of the polynomial.) If d < 0 there are no real roots. Instead, it has two complex roots which will be conjugates of one another.
What is x to the second power plus x to the fifth power?
It is a fifth order polynomial. The two terms cannot be combined, except to factor out x² and get x²(x³ + 1). This can be solved for 5 roots: 0, 0, -1, and two complex roots: 1/2 ± i(√3)/2
A polynomial with two terms?
It is binomial
Which two values of x are roots of the polynomial below x2 plus 5x plus 11?
There are none because the discriminant of the given quadratic expression is less than zero.
Which two values of x are roots of the polynomial x2 plus 5x plus 9?
-2.5 + 1.6583123951777i-2.5 - 1.6583123951777i
X2-11x plus 13 has two values of x are roots of a polynomial what is it?
x=11+69/2 and x=11-69/2
Which two values of x are roots of the polynomial x2 plus 3x - 5?
x2 + 3x - 5 is an expression, not an equation. An equation may have roots, an expression does not. However, x2 + 3x - 5 = 0 is an equation and its roots are -4.1926 and 1.1926 (approx).
Which two values of x are roots of the polynomial below x2-3x 5?
It is difficult to tell because there is no sign (+ or -) before the 5. +5 gives complex roots and assuming that someone who asked this question has not yet come across complex numbers, I assume the polynomial is x2 -3x - 5 The roots of this equation are: -1.1926 and 4.1926 (to 4 dp)
How to tell if there are no real roots?
The real roots of what, exactly? If you mean a square trinomial, then: If the discriminant is positive, the polynomial has two real roots. If the discriminant is zero, the polynomial has one (double) real root. If the discriminant is negative, the polynomial has two complex roots (and of course no real roots). The discriminant is the term under the square root in the quadratic equation, in other words, b2 - 4ac.
Which two values of x are roots of the polynomial below x2 plus 5x plus 9?
x = -2.5 + 1.6583123951777ix = -2.5 - 1.6583123951777iwhere i is the square root of negative one.
What is the relationship between the degree of a polynomial and the number of roots it has?
In answering this question it is important that the roots are counted along with their multiplicity. Thus a double root is counted as two roots, and so on. The degree of a polynomial is exactly the same as the number of roots that it has in the complex field. If the polynomial has real coefficients, then a polynomial with an odd degree has an odd number of roots up to the degree, while a polynomial of even degree has an even number of roots up to the degree. The difference between the degree and the number of roots is the number of complex roots which come as complex conjugate pairs.
The graph of a polynomial changes direction twice and has only one root What can you say about the polynomial?
It is a polynomial of odd power - probably a cubic. It has only one real root and its other two roots are complex conjugates. It could be a polynomial of order 5, with two points of inflexion, or two pairs of complex conjugate roots. Or of order 7, etc.
How do the zeros of a polynomial function help you determine the answer?
They tell you where the graph of the polynomial crosses the x-axis.Now, taking the derivative of the polynomial and setting that answer to zero tells you where the localized maximum and minimum values occur. Two values that have vast applications in almost any profession that uses statistics.
How do you do a parabola?
A parabola is a graph of a 2nd degree polynomial function. Two graph a parabola, you must factor the polynomial equation and solve for the roots and the vertex. If factoring doesn't work, use the quadratic equation.
How many real roots do we have if the polynomial equation is in degree six?
Such an equation has a total of six roots; the number of real roots must needs be even. Thus, depending on the specific equation, the number of real roots may be zero, two, four, or six.
