What equation has no real roots?
If a quadratic equation has no real roots then its discriminant is less than zero. The discriminant of general quadratic equation ax2+bx+c=0 is b2−4ac .
What quadratic equation has no real roots?
A quadratic equation ax² + bx + c = 0 has no real roots when the discriminant of the equation is less than zero. Therefore, the equation has no real roots.
Can a quadratic equation have no roots?
If you say no real roots, then the answer is yes. But if you say no roots in any domain then the answer is no. If you have no real roots, you still have imaginary roots. The roots of this equation are +i and -i.
How do you find the vertex without roots?
Solution
- Get the equation in the form y = ax2 + bx + c.
- Calculate -b / 2a. This is the x-coordinate of the vertex.
- To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.
How do you prove a quadratic equation has no real roots?
If the discriminant is greater than zero, this means that the quadratic equation has no real roots. Therefore, there are no real roots to the quadratic equation 3×2 + 2x + 1. If the discriminant is equal to zero, this means that the quadratic equation has two real, identical roots.
For what value of k equation has no real roots?
To have no real roots means discriminant should be less than zero. Therefore, for k<-9 the quadratic equation will have no real roots.
What happens when discriminant is 0?
A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.
What are no real solutions?
There is a special case that will tell us if a quadratic has no real solution: if b = 0 when a and c share the same sign (both positive or both negative), then there will be no real solution. The quadratic formula becomes much simpler when b = 0.
For what value of k the equation has no real roots?
What is value of k if the roots of are real and equal?
The value of k for which the roots are real and equal of the following equation. k2x2 – 2(2k – 1) x + 4 = 0 is k = 41.
What does no real roots mean?
Case 1: No Real Roots If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.
When discriminant of a quadratic is zero its both roots are?
If the discriminant is equal to zero, this means that the quadratic equation has two real, identical roots. Therefore, there are two real, identical roots to the quadratic equation x2 + 2x + 1.
Do all parabolas have roots?
Thus, a parabola has exactly one real root when the vertex of the parabola lies right on the x-axis. The simplest example of a quadratic function that has only one real root is, y = x2, where the real root is x = 0.
What are the roots of a parabola?
The roots are the x-intercepts, where the parabola crosses the x-axis. If the parabola opens up and it’s vertex is below the x-axis then it crosses the x-axis in two places and has two (real) roots. If the vertex is on the x-axis then the parabola has one root.
Why does an equation have no real solutions?
The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur. Use distributive property on the right side first.