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where the discriminant is zero if and only if the two roots are equal. If a, b, c are real numbers, the polynomial has two distinct real roots if the discriminant is positive, and two complex conjugate roots if it is negative. [6] The discriminant is the product of a 2 and the square of the difference of the roots.
Figure 1. Plots of quadratic function y = ax 2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0). A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots.
Structure Correlation Coefficients: The correlation between each predictor and the discriminant score of each function. This is a zero-order correlation (i.e., not corrected for the other predictors). [15] Standardized Coefficients: Each predictor's weight in the linear combination that is the discriminant function.
Specific difficulties include catastrophic cancellation in computing the sum if ; catastrophic calculation in computing the discriminant = itself in cases where ; degeneration of the formula when , , or is represented as zero or infinite; and possible overflow or underflow when multiplying or ...
The discriminant of a quadratic form, concretely the class of the determinant of a representing matrix in K / (K ×) 2 (up to non-zero squares) can also be defined, and for a real quadratic form is a cruder invariant than signature, taking values of only "positive, zero, or negative".
The discriminant is zero when = ... is defined to be the difference between the 'expected' number + and the number of points on the ...
Coke Zero was reformulated last summer, and in my Coke Zero review, I wasn’t afraid to say I didn’t love the new formula. I found it almost sour, with a spiciness that older Coke Zero didn’t ...
In particular, if the determinant is zero, then this parallelotope has volume zero and is not fully n-dimensional, which indicates that the dimension of the image of A is less than n. This means that A produces a linear transformation which is neither onto nor one-to-one, and so is not invertible.