How do you show an equation has no real roots?
How do you show an equation has 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….
- b2 −4ac < 0 There are no real roots.
- b2 −4ac = 0 There is one real root.
- b2 −4ac > 0 There are two real roots.
How do you prove an equation has no real solutions?
Look At The Discriminant. The first way to tell if a quadratic has no real solution is to look at the discriminant. If the discriminant is negative, then the quadratic equation has no real solution. The discriminant is the expression b2 – 4ac under the radical in the quadratic formula.
How many real roots does the equation x2 2 2 x2 0 have?
Answer: The original equation has NO real roots.
For what value of A has no real roots?
Explanation: 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 .
How do you find the real roots?
You can find the roots, or solutions, of the polynomial equation P(x) = 0 by setting each factor equal to 0 and solving for x. Solve the polynomial equation by factoring. Set each factor equal to 0. 2×4 = 0 or (x – 6) = 0 or (x + 1) = 0 Solve for x.
What can you say about see if the equation has exactly one solution?
If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent .
How many roots does x2 1/2 x2 have?
Hence, the equation (x2 + 1)2 – x2 = 0 has no real roots.
How do you find the real roots of an equation?
Is 0 A real root?
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. D > 0 means two real, distinct roots. D < 0 means no real roots.