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Which two values of x are roots of the polynomial x2-11x 15?
To find the roots of the polynomial (x^2 - 11x + 15), we can factor it as ((x - 5)(x - 3) = 0). Setting each factor equal to zero gives us the roots (x = 5) and (x = 3). Thus, the two values of (x) that are roots of the polynomial are (3) and (5).
The points plotted below are on the graph of a polynomial. In what range of values must the polynomial have a root?
To determine the range of values where the polynomial must have a root, you need to apply the Intermediate Value Theorem. This theorem states that if a polynomial takes on opposite signs at two points, then it must cross the x-axis (i.e., have a root) somewhere between those two points. Therefore, by examining the plotted points and identifying intervals where the values of the polynomial change sign, you can pinpoint the ranges where roots are guaranteed to exist.
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 of x2 plus 5x plus 9?
To find the roots of the polynomial (x^2 + 5x + 9), we can use the quadratic formula: (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}). Here, (a = 1), (b = 5), and (c = 9). The discriminant (b^2 - 4ac = 5^2 - 4 \cdot 1 \cdot 9 = 25 - 36 = -11), which is negative. This means the polynomial has no real roots, but two complex roots: (x = \frac{-5 \pm i\sqrt{11}}{2}).
What is the polynomial having two terms?
A polynomial with two terms is called a binomial.
Which two values of x are roots of the polynomial x2-11x 15?
To find the roots of the polynomial (x^2 - 11x + 15), we can factor it as ((x - 5)(x - 3) = 0). Setting each factor equal to zero gives us the roots (x = 5) and (x = 3). Thus, the two values of (x) that are roots of the polynomial are (3) and (5).
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
The points plotted below are on the graph of a polynomial. In what range of values must the polynomial have a root?
To determine the range of values where the polynomial must have a root, you need to apply the Intermediate Value Theorem. This theorem states that if a polynomial takes on opposite signs at two points, then it must cross the x-axis (i.e., have a root) somewhere between those two points. Therefore, by examining the plotted points and identifying intervals where the values of the polynomial change sign, you can pinpoint the ranges where roots are guaranteed to exist.
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
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 x2-3x 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)
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.
Which two values of x are roots of the polynomial of x2 plus 5x plus 9?
To find the roots of the polynomial (x^2 + 5x + 9), we can use the quadratic formula: (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}). Here, (a = 1), (b = 5), and (c = 9). The discriminant (b^2 - 4ac = 5^2 - 4 \cdot 1 \cdot 9 = 25 - 36 = -11), which is negative. This means the polynomial has no real roots, but two complex roots: (x = \frac{-5 \pm i\sqrt{11}}{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).
