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Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals?
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What is Nature of the zeros of a quadratic function?
If you have a quadratic function with real coefficients then it can have: two distinct real roots, or a real double root (two coincidental roots), or no real roots. In the last case, it has two complex roots which are conjugates of one another.
When the discriminant is positive the answer to the quadratic equation will be?
Then x will have two different distinct roots
A positive discriminant means the quadratic equation will have how many solutions?
Two distinct real solutions.
What is the formula for finding the value of x in the quadratic equation ax2 bx c0?
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. However, assuming your question to find the roots or solutions of ax2 + bx + c = 0, the answer is x = [-b ± sqrt(b2 - 4ac)]/2a b2 - 4ac is called the discriminant. If the discriminant > 0 then the quadratic equation has two distinct real roots. If the discriminant = 0 then the quadratic equation has one double root. If the discriminant < 0 then the quadratic equation has two distinct complex roots that are conjugates of one another.
Could you ever have three solutions to a quadratic equation?
No. By definition, a quadratic equation can have at most two solutions. For a quadratic of the form ax^2 + bx + c, when the discriminant of a quadratic, b^2 - 4a*c is positive you have two distinct real solutions. As the discriminant becomes smaller, the two solutions move closer together. When the discriminant becomes zero, the two solutions coincide which may also be considered a quadratic with only one solution. When the discriminant is negative, there are no real solutions but there will be two complex solutions - that is those involving i = sqrt(-1).
What is Nature of the zeros of a quadratic function?
If you have a quadratic function with real coefficients then it can have: two distinct real roots, or a real double root (two coincidental roots), or no real roots. In the last case, it has two complex roots which are conjugates of one another.
What are quadratic equations?
In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is : where a≠ 0. (For if a = 0, the equation becomes a linear equation.) The letters a, b, and c are called coefficients: the quadratic coefficient a is the coefficient of x2, the linear coefficient b is the coefficient of x, and c is the constant coefficient, also called the free term or constant term. Quadratic equations are called quadratic because quadratus is Latin for "square"; in the leading term the variable is squared. A quadratic equation with real or complex coefficients has two (not necessarily distinct) solutions, called roots, which may or may not be real, given by the quadratic formula: : where the symbol "±" indicates that both : and are solutions.
When the discriminant is positive the answer to the quadratic equation will be?
Then x will have two different distinct roots
In general how many distinct solutions are there to a quadratic equation?
the maximum number of solutions to a quadratic equation is 2. However, usually there is only 1.
A positive discriminant means the quadratic equation will have how many solutions?
Two distinct real solutions.
Is there a rational number between any two distinct rational numbers?
Yes. Not only that, but there are an infinite number of rationals between any two distinct rationals - however close. We can prove it like this: Take any three rational numbers, call them A, B and C, where B is larger than A, and C is any rational number greater than 1: D = A + (B - A) / C That gives us another rational number, D, no matter what the values of the original numbers are.
How do you know if a quadratic equation will have more than one solutions?
Write the quadratic equation in the standard form: ax2 + bx + c = 0 Then calculate the discriminant = b2 - 4ac If the discriminant is greater than zero, there are two distinct real solutions. If the discriminant is zero, there is one real solution. If the discriminany is less than zero, there are no real solutions (there will be two distinct imaginary solutions).
What is the formula for finding the value of x in the quadratic equation ax2 bx c0?
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. However, assuming your question to find the roots or solutions of ax2 + bx + c = 0, the answer is x = [-b ± sqrt(b2 - 4ac)]/2a b2 - 4ac is called the discriminant. If the discriminant > 0 then the quadratic equation has two distinct real roots. If the discriminant = 0 then the quadratic equation has one double root. If the discriminant < 0 then the quadratic equation has two distinct complex roots that are conjugates of one another.
Using the word discriminant in sentence?
The discriminant of a quadratic equation helps determine the nature of its roots - whether they are real and distinct, real and equal, or imaginary.
What is true about a quadratic equation when the discriminant of the equation is positive?
It will then have 2 different roots If the discriminant is zero than it will have have 2 equal roots
Could you ever have three solutions to a quadratic equation?
No. By definition, a quadratic equation can have at most two solutions. For a quadratic of the form ax^2 + bx + c, when the discriminant of a quadratic, b^2 - 4a*c is positive you have two distinct real solutions. As the discriminant becomes smaller, the two solutions move closer together. When the discriminant becomes zero, the two solutions coincide which may also be considered a quadratic with only one solution. When the discriminant is negative, there are no real solutions but there will be two complex solutions - that is those involving i = sqrt(-1).
What does the discriminant tell you when solving quadratic equations for the roots?
Whether the equation has 2 distinct roots, repeated roots, or complex roots. If the determinant is smaller than 0 then it has complex roots. If the determinant is 0 then it has repeated roots. If the determinant is greater than 0 then it has two distinct roots.
