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 ax2 + bx + c = 0, plug the coefficients into the expression b2 – 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 ax2 + bx + c = 0 is given by the quadratic formula x = [-b ± √(b2 – 4ac)] / 2a, to find the solution of a quadratic equation. In the case of one real solution, the value of discriminant b2 – 4ac is zero. For example, x2 + 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.
find real solutions of quadratic equation
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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 4x2 + 26x + 12 = 0, its discriminant is equals to b2 − 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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