Which quadratic has no real roots?
The value of the discriminant shows how many roots f(x) has: – If b2 – 4ac > 0 then the quadratic function has two distinct real roots. – If b2 – 4ac = 0 then the quadratic function has one repeated real root. – If b2 – 4ac < 0 then the quadratic function has no real roots.
Is it possible for a quadratic inequality not to have a real solution?
Quadratic inequalities can have infinitely many solutions, one solution or no solution. We can solve quadratic inequalities graphically by first rewriting the inequality in standard form, with zero on one side.
What equation has no real roots?
Solution: A quadratic equation ax2 + bx + c = 0 has no real roots if discriminant < 0.
How do you know if it is a quadratic inequality or not?
A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. Examples of quadratic inequalities are: x2 – 6x – 16 ≤ 0, 2×2 – 11x + 12 > 0, x2 + 4 > 0, x2 – 3x + 2 ≤ 0 etc. Solving a quadratic inequality in Algebra is similar to solving a quadratic equation.
How do you find a quadratic equation has real roots?
For a quadratic equation ax2 + bx + c = 0, The roots are calculated using the formula, x = (-b ± √ (b² – 4ac) )/2a. Discriminant is, D = b2 – 4ac. If D > 0, then the equation has two real and distinct roots.
How can an inequality have no solution?
Some inequalities do not have a solution. When two inequalities have parallel lines and the shaded areas do not overlap (i.e., the opposite areas are shaded), then the system has no solution. This means that there is no coordinate point that makes both inequalities true.
For what value of a the quadratic equation 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 .
Which of the following quadratic equations has no real solutions?
2 Answers By Expert Tutors The equation Ax2 + Bx + C = 0 has no real solutions when the discriminant is negative.
How are the quadratic inequalities used in solving real life problems and in making decisions?
Quadratic equations are actually used in everyday life, as when calculating areas, determining a product’s profit or formulating the speed of an object. Quadratic equations refer to equations with at least one squared variable, with the most standard form being ax² + bx + c = 0.
How do you find real roots?
Here’s how Descartes’s rule of signs can give you the numbers of possible real roots, both positive and negative:
- Positive real roots. For the number of positive real roots, look at the polynomial, written in descending order, and count how many times the sign changes from term to term.
- Negative real roots.