First put your equation into standard form,
then
Find the Discriminant,
No calculation quick look: If the signs on
John
My calculator said it, I believe it, that settles it
25 + 4x² = -20x
discriminant
how do you find the determinant then the number of rational, irrational or complex roots??25 + 4x² = -20x how do you find thedeterminantthen the number of rational, irrational or complex roots?? The word is "discriminant", not "determinant". First you get the quadratic equation in descending order with 0 on the right. 25 + 4x² = -20x 4x² + 20x + 25 = 0 Compare that to the general quadratic equation: ax² + bx + c = 0 If you remember the quadratic formula,then you already know the discriminant formula because it is what is under the aquare root part of the quadratic formula. Discriminant = b² - 4ac Comparing your equation to the general quadratic equation, a = 4, b = 20, c = 25 Substitute in the discriminant formula: Discriminant = b² - 4ac Discriminant = (20)² - 4(4)(25) Discriminant = 400 - 400 Discriminant = 0 The rules are 1. If the discriminant is positive there are 2 real roots A. If the discriminant is a perfect square, both roots are rational B. If the discriminant is not a perfect square, both roots are irrational. 2. If the discriminant is negative, there are 2 conjugate complex roots. 3. If the discriminant is 0, there is just one real rational root. Your problem is case 3, so there is one real rational root. Edwin