![]() What is the Formula for Discriminant of Cubic Equation?Ī cubic equation is of the form ax 3 + bx 2 + cx + d = 0 and its discriminant is in terms of its coefficients which is given by the formula D = b 2c 2 − 4ac 3 − 4b 3d − 27a 2d 2 + 18abcd. If the discriminant of a quadratic equation ax 2 + bx + c = 0 is negative (i.e., if b 2 - 4ac < 0), then the quadratic formula becomes x = (-b ± √(negative number) ) / 2a and hence the quadratic equation has only two complex and distinct roots. If the discriminant of a quadratic equation ax 2 + bx + c = 0 is positive (i.e., if b 2 - 4ac > 0), then the quadratic formula becomes x = (-b ± √(positive number) ) / 2a and hence the quadratic equation has only two real and distinct roots. If the discriminant of a quadratic equation ax 2 + bx + c = 0 is 0 (i.e., if b 2 - 4ac = 0), then the quadratic formula becomes x = -b/2a and hence the quadratic equation has only one real root. ![]() Substitute the values in the discriminant formula D = b 2 − 4ac.Identify a, b, and c by comparing the given equation with ax 2 + bx + c = 0.To calculate the discriminant of a quadratic equation: How to Calculate the Discriminant of a Quadratic Equation? syms u v eqns 2u + v 0, u - v 1 S solve (eqns, u v) S struct with fields: u: 1/3 v: -2/3. Solve a system of equations to return the solutions in a structure array. The discriminant of a cubic equation ax 3 + bx 2 + cx + d = 0 is Δ or D = b 2c 2 − 4ac 3 − 4b 3d − 27a 2d 2 + 18abcd. The solve function returns a structure when you specify a single output argument and multiple outputs exist. The discriminant of a quadratic equation ax 2 + bx + c = 0 is Δ OR D = b 2 − 4ac. There re different discriminant formulas for different polynomials: Whether the roots are real or non-real?.For example, the discriminant of a quadratic equation is used to find: It tells the nature of roots or in other words, it discriminates the roots. The discriminant in math is defined for polynomials and it is a function of coefficients of polynomials. (iii) no real roots or two complex roots when D < 0įAQs on Discriminant What is Discriminant Meaning? So when the discriminant of a quadratic equation is greater than 0, it has two roots which are distinct and real numbers. i.e.,ĭo you recall using b 2 − 4ac earlier? Yes, it is a part of the quadratic formula: x = \(\dfrac\) and the square root of a positive number always results in a real number. The discriminant of a quadratic equation ax 2 + bx + c = 0 is in terms of its coefficients a, b, and c. Then we substitute the coefficients in the relevant formula to find the discriminant. To find the discriminant of a cubic equation or a quadratic equation, we just have to compare the given equation with its standard form and determine the coefficients first.
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