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What is the name of the number under the radical symbol in the quadratic formula?
The discriminant
What does it mean if the value under the radical sign in the quadratic formula is negative?
If the value under the radical sign (the discriminant) in the quadratic formula is negative, it means that the quadratic equation has no real solutions. Instead, it has two complex (or imaginary) solutions. This occurs because the square root of a negative number is not defined in the set of real numbers, indicating that the parabola represented by the equation does not intersect the x-axis.
How do you solve complex cases of quadratic equations?
If the discriminant - the part under the radical sign in the quadratic formula - is negative, then the result is complex, it is as simple as that. You can't convert a complex number to a real number. If a particular problem requires only real-number solutions, then - if the formula gives complex numbers - you can state that there is no solution.
Can you add or subtract under the radical?
No, you cannot add or subtract under the radical. The radical represents the square root function, and it only operates on the number or expression that is inside the radical. To add or subtract, you need to simplify the expressions inside the radical first.
How can you say that radical expression is already in the simplified form?
A radical expression is considered to be in simplified form when there are no perfect square factors (or higher-order factors, depending on the root) remaining under the radical, and no fractions exist within the radical itself. Additionally, any coefficients in front of the radical should be as simple as possible, and the index of the radical should be minimal. If these conditions are met, the expression is deemed simplified.
What is the expression b2 4ac under the radical sign in the quadratic formula?
The discriminant.
The is the name of the number under the radical symbol in the quadratic formula?
discriminant
What is the name of the number under the radical symbol in the quadratic formula?
The discriminant
What does it mean if the value under the radical sign in the quadratic formula is negative?
If the value under the radical sign (the discriminant) in the quadratic formula is negative, it means that the quadratic equation has no real solutions. Instead, it has two complex (or imaginary) solutions. This occurs because the square root of a negative number is not defined in the set of real numbers, indicating that the parabola represented by the equation does not intersect the x-axis.
What is the expression b2-4ac under the radical sign in the quadratic formula?
6
What is the expression under the radical called?
radicand
How do you solve complex cases of quadratic equations?
If the discriminant - the part under the radical sign in the quadratic formula - is negative, then the result is complex, it is as simple as that. You can't convert a complex number to a real number. If a particular problem requires only real-number solutions, then - if the formula gives complex numbers - you can state that there is no solution.
Can you add or subtract under the radical?
No, you cannot add or subtract under the radical. The radical represents the square root function, and it only operates on the number or expression that is inside the radical. To add or subtract, you need to simplify the expressions inside the radical first.
How can you say that radical expression is already in the simplified form?
A radical expression is considered to be in simplified form when there are no perfect square factors (or higher-order factors, depending on the root) remaining under the radical, and no fractions exist within the radical itself. Additionally, any coefficients in front of the radical should be as simple as possible, and the index of the radical should be minimal. If these conditions are met, the expression is deemed simplified.
How many roots can a quadratic function have in total?
A quadratic function can have up to two roots. Depending on the discriminant (the expression under the square root in the quadratic formula), it can have two distinct real roots, one repeated real root, or no real roots at all (in which case the roots are complex). Therefore, the total number of roots, considering both real and complex, is always two.
How are radical expression's simplified?
The details depend on the specific radical expression. Normally, you'll want to: * Avoid a perfect square under a radical sign. Take it out, by separating the radical into two parts. Example: root (x squared y) = root (x squared) x root (y) = x root (y). * Avoid a radical sign in the denominator. If you multiply numerator and denominator by the same square root, you get an expression in which there are roots in the numerator, but not in the denominator.
How do you symplify radical expressions?
Suppose the expression under the radical sign is y. Then the first step is to simplify y. Next find a term (or expression) x, such that y = x^2*z for some term (or expression) z. Then x*sqrt(z) is a simplification of sqrt(y).
