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Given the quadratic equation ax^2 + bx + c =0, where a, b, and c are real numbers:
(The discriminant is equal to b^2 - 4ac)
If b^2 - 4ac < 0, there are two conjugate imaginary roots.
If b^2 - 4ac = 0, there is one real root (called double root)
If b^2 - 4ac > 0, there are two different real roots.
In the special case when the equation has integral coefficients (means that all coefficients are integers), and b^2 - 4ac is the square of an integer, the equation has rational roots. That is , if b^2 - 4ac is the square of an integer, then ax^2 + bx + c has factors with integral coefficients.
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Strictly speaking, the last part of the last sentence is not true.
For example, consider the equation 4x2 + 8x + 3 = 0
the discriminant is 16, which is a perfect square and the equation can be written as (2x+1)*(2x+3) = 0
To that extent the above is correct.
However, the equation can also be written, in factorised form, as (x+1/2)*(x+3/2) = 0 Not all integral coefficients.
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Find the discriminant for 2x2 - 3x - 5 0?
The discriminant is 49.
Find the value of the discriminant of each equation given X2 - 5x plus 4 equals 0?
The discriminant is 9.
Is it possible to find the discriminant of a binomial?
A polynomial discriminant is defined in terms of the difference in the roots of the polynomial equation. Since a binomial has only one root, there is nothing to take its difference from and so in such a situation, the discriminant is a meaningless concept.
How do you find the discriminant of a equation?
The general form of a quadratic equation is ax2 + bx + c = 0 where a is not zero, a, b and c are constants. The discriminant is b2 - 4ac
Find the discriminant of the polynomial below 2x2 plus 3x-7?
65
Find the discriminant for 2x2 - 3x - 5 0?
The discriminant is 49.
How do you find how many x intercepts the parabola has using the discriminant?
If the discriminant is negative, there are 0 interceptsIf the discriminant is zero, there is 1 interceptIf the discriminant is positive, there are 2 intercepts
How do you find the discriminant of a function?
To find the discriminant of a quadratic function, first express it in descending powers, thusax^2 + bx + c = 0 where a, b and c are real and a is non-zero.Then the discriminant is b^2 - 4ac
Find the value of the discriminant of each equation given X2 - 5x plus 4 equals 0?
The discriminant is 9.
What do you find when you determine the discriminant?
Whether or not that there is a solution to a quadratic equation,
Is it possible to find the discriminant of a binomial?
A polynomial discriminant is defined in terms of the difference in the roots of the polynomial equation. Since a binomial has only one root, there is nothing to take its difference from and so in such a situation, the discriminant is a meaningless concept.
Find the discriminant of the polynomial 2x2 plus 4x-9?
The discriminant is 88 which means that the given quadratic equation has two different solutions for x
How do you find the discriminant of a equation?
The general form of a quadratic equation is ax2 + bx + c = 0 where a is not zero, a, b and c are constants. The discriminant is b2 - 4ac
Find the discriminant of the polynomial below 2x2 plus 3x-7?
65
What does the discriminant tell you?
The discriminant tells you how many solutions there are to an equation The discriminant is b2-4ac For example, two solutions for a equation would mean the discriminant is positive. If it had 1 solution would mean the discriminant is zero If it had no solutions would mean that the discriminant is negative
How do you tell if a discriminant is positive negative or zero?
With the standard notation, If b2 < 4ac then the discriminant is negative If b2 = 4ac then the discriminant is zero If b2 > 4ac then the discriminant is positive
What is a discriminant and how does help to solve equations?
In the quadratic formula, the discriminant is b2-4ac. If the discriminant is positive, the equation has two real solutions. If it equals zero, the equation has one real solution. If the discriminant is negative, it has two imaginary solutions. This is because you find the square root of the discriminant and add or subtract it from -b and divide the sum or difference by 2a. If the square root is of a positive number, then you get two different solutions, one from adding the discriminant to -b and one from subtracting the discriminant from -b. If the square root is of zero, then it equals zero, and the solution is -b/2a. If the square root is of a negative number, then you have two imaginary solutions because you can't take the square root of a negative number and get a real number. One solution is from subtracting the discriminant from -b and dividing by 2a, and the other is from adding it to -b and dividing by 2a. The parabola on the left has a positive discriminant. The parabola in the middle has a discriminant of zero. The parabola on the right has a negative discriminant.
