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The discriminant is the expression inside the square root of the quadratic formula. For a quadratic ax² + bx + c = 0, the quadratic formula is x = (-b +- Sqrt(b² - 4ac))/(2a). The expression (b² - 4ac) is the discriminant. This can tell a lot about the type of roots. First, if the discriminant is a negative number, then it will have two complex roots. Because you have a real number plus sqrt(negative) and real number minus sqrt(negative).
You asked about irrational. If the discrimiant is a perfect square number {like 1, 4, 9, 16, etc.} then the quadratic will have two distinct rational roots (which are real numbers). If the discriminant is zero, then you will have a double root, which is a real rational number.
So if the discrimiant is positive, but not a perfect square, then the roots will be irrational real numbers. If the discriminant is a negative number which is not the negative of a perfect square, then imaginary portion of the complex number will be irrational.
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What indicates that the roots of a quadratic are irrational?
In the quadratic equation, b^2 - 4ac < 0.
What indicates if the roots of a quadratic square are irrational?
If the determinant of the quadratic (ax² + bc + c) as worked out by b² - 4ac is a perfect square or not. If the determinant is not a perfect square then the roots are irrational.
Does there exist a quadratic equation whose coefficients are irrational but both the roots are rational?
None, if the coefficients of the quadratic are in their lowest form.
What does the discriminant have to be in order for the roots of a quadratic to be irrational?
The discriminant must be a positive number which is not a perfect square.
What is x to the power of 2 plus 10X minus 4 factored?
There is no simple factorisation because the quadratic expression does not have rational roots. Irrational roots are not used in factorisation.
What indicates that the roots of a quadratic are irrational?
In the quadratic equation, b^2 - 4ac < 0.
What indicates if the roots of a quadratic square are irrational?
If the determinant of the quadratic (ax² + bc + c) as worked out by b² - 4ac is a perfect square or not. If the determinant is not a perfect square then the roots are irrational.
Does there exist a quadratic equation whose coefficients are irrational but both the roots are rational?
None, if the coefficients of the quadratic are in their lowest form.
What does the discriminant have to be in order for the roots of a quadratic to be irrational?
The discriminant must be a positive number which is not a perfect square.
How do you factor p2 plus 2p-7 equals 0?
The quadratic cannot be factorised. Its roots are irrational.
What is x to the power of 2 plus 10X minus 4 factored?
There is no simple factorisation because the quadratic expression does not have rational roots. Irrational roots are not used in factorisation.
What are quadratic equations with real roots?
If the discriminant of the quadratic equation is zero then it will have 2 equal roots. If the discriminant of the quadratic equation is greater than zero then it will have 2 different roots. If the discriminant of the quadratic equation is less than zero then it will have no roots.
What are the roots of a quadratic?
The roots of a quadratic function are where the lies interescts with the x-axis. There can be as little as zero.
Why do you use square roots to solve quadratic equations?
Because it's part of the quadratic equation formula in finding the roots of a quadratic equation.
How many roots does a quadratic equation?
2 roots
What are the roots of the quadratic equation below?
That depends on the equation.
What is the graph of a quadratic formula?
In general, quadratic equations have graphs that are parabolas. The quadratic formula tells us how to find the roots of a quadratic equations. If those roots are real, they are the x intercepts of the parabola.
