Let’s discuss the question: how to determine if a quadratic equation has real solutions. We summarize all relevant answers in section Q&A of website Achievetampabay.org in category: Blog Finance. See more related questions in the comments below.

## How do you tell if an equation has a real solution?

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Given a quadratic equation ax^{2} + bx + c = 0, plug the coefficients into the expression b^{2} – 4ac to see what results: **If you get a positive number, the quadratic will have two unique solutions**. If you get 0, the quadratic will have exactly one solution, a double root.

## How do you find the real solution of a quadratic equation?

The solution of a quadratic equation ax^{2} + bx + c = 0 is given by the quadratic formula x = [-b ± √(b^{2} – 4ac)] / 2a, to find the solution of a quadratic equation. In the case of one real solution, **the value of discriminant b ^{2} – 4ac is zero**. For example, x

^{2}+ 2x + 1 = 0 has only one solution x = -1.

### Using Discriminants to Determine the Number of Real Solutions to Quadratic Equations

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## What does it mean when a quadratic has no real solutions?

**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.

## Do quadratic equations always have two real solutions?

**A quadratic equation with real or complex coefficients has two solutions**, called roots. These two solutions may or may not be distinct, and they may or may not be real.

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## How many real solutions does this quadratic have?

The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. **A positive discriminant indicates that the quadratic has two distinct real number solutions**. A discriminant of zero indicates that the quadratic has a repeated real number solution.

## What is an example of one real solution?

For example, in the quadratic equation 4x^{2} + 26x + 12 = 0, its discriminant is equals to b^{2} − 4ac = (26)^{2} − 4(4)(12) = 484 which is positive and so the equation has two real solutions. **If the discriminant is zero, then there is exactly one real solution**.

## What does it mean if an equation has no real solutions?

“No solution” means that **there is no value, not even 0, which would satisfy the equation**. Also, be careful not to make the mistake of thinking that the equation 4 = 5 means that 4 and 5 are values for x that are solutions.

### Can You Determine if a Quadratic Equation has Real Roots? If so, Find the Roots – Simple Tutorial

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## Why do quadratics have two solutions?

**A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero**, So there exist two solution.

## What are real solutions?

In chemistry, a real solution is **a homogeneous mixture of at least two chemical substances**. A “real” solution differs from a colloidal solution (colloid). According to the concentration of the solute, a distinction is made between hypotonic solution, saturated solution, unsaturated solution.

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