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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.
What else can I help you with?
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
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
Find the discriminant of the polynomial below 2x2 plus 3x-7?
65
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 the discriminant of the polynomial 2x2 5x 4?
The discriminant is -7
