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Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals?
Yes, it is possible for a quadratic equation to have distinct irrational coefficients while having rational roots. For example, consider the quadratic equation (x^2 - \sqrt{2}x - \sqrt{3} = 0). The coefficients (-\sqrt{2}) and (-\sqrt{3}) are distinct irrationals, yet the roots of this equation can be rational. Specifically, if we apply the quadratic formula, we can find rational roots depending on the specific values of the coefficients.
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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.
Why the quadratic equation has only one distinct solution?
A quadratic equation has only one distinct solution when its discriminant (the part of the equation under the square root in the quadratic formula) is zero. This occurs when the equation can be expressed in the form ( (x - r)^2 = 0 ), where ( r ) is the repeated root. In this case, the parabola touches the x-axis at a single point, indicating that there is only one unique solution. Thus, the equation has a double root, rather than two distinct solutions.
Explain how to solve a quadratic equation explain how to determine and find the different types of solutions. describe at least two differents methods ( graphing factoring or quadratic formula?
To solve a quadratic equation, you can use methods like factoring, graphing, or the quadratic formula. Factoring involves rewriting the equation as a product of binomials, allowing you to set each factor to zero and solve for the variable. Graphing involves plotting the quadratic function and identifying the x-intercepts, which represent the solutions. The quadratic formula, ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ), provides the solutions directly from the coefficients of the equation ( ax^2 + bx + c = 0 ), where the discriminant ( b^2 - 4ac ) indicates the nature of the solutions: two real and distinct, one real and repeated, or two complex.
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.
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.
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.
Why the quadratic equation has only one distinct solution?
A quadratic equation has only one distinct solution when its discriminant (the part of the equation under the square root in the quadratic formula) is zero. This occurs when the equation can be expressed in the form ( (x - r)^2 = 0 ), where ( r ) is the repeated root. In this case, the parabola touches the x-axis at a single point, indicating that there is only one unique solution. Thus, the equation has a double root, rather than two distinct solutions.
Explain how to solve a quadratic equation explain how to determine and find the different types of solutions. describe at least two differents methods ( graphing factoring or quadratic formula?
To solve a quadratic equation, you can use methods like factoring, graphing, or the quadratic formula. Factoring involves rewriting the equation as a product of binomials, allowing you to set each factor to zero and solve for the variable. Graphing involves plotting the quadratic function and identifying the x-intercepts, which represent the solutions. The quadratic formula, ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ), provides the solutions directly from the coefficients of the equation ( ax^2 + bx + c = 0 ), where the discriminant ( b^2 - 4ac ) indicates the nature of the solutions: two real and distinct, one real and repeated, or two complex.
What is the solution of ax2 bx c 0?
The solution to the quadratic equation ( ax^2 + bx + c = 0 ) can be found using the quadratic formula: ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ). Here, ( a ), ( b ), and ( c ) are coefficients, and the term ( b^2 - 4ac ) is called the discriminant, which determines the nature of the roots. If the discriminant is positive, there are two distinct real solutions; if it is zero, there is one real solution (a double root); and if it is negative, there are two complex 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.
Does a quadratic equation always have two solutions?
A quadratic equation can have two solutions, one solution, or no real solutions, depending on its discriminant (the part of the quadratic formula under the square root). If the discriminant is positive, there are two distinct real solutions; if it is zero, there is exactly one real solution (a repeated root); and if it is negative, there are no real solutions, only complex ones. Thus, a quadratic equation does not always have two solutions.
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.
