What type of roots are obtained when the discriminant is positive?

given the nature of the roots, to find the condition that makes this happen. Find the nature of the roots of 9x² +24x+16=0. a = 9 b=24 c = 16 b2-4ac ... b2 – 4ac < 0. No real roots. 4. b2 – 4ac = 32- 4x1x(-2) = 9 +8 = 17. b2 ... If b2 – 4ac < 0 , the line does not touch the curve. It is not a tangent. If ... However, we know there must be another independent solution. It's not obvious what that might be, but let's make the educated guess y(t) = C2teλ1t. 2. Simple Gini Index with Quadratic Pen's Parade. Consider a quadratic ... b2 – 4ac < 0. We are now able to compute the coefficient of variation of ... (Algebra: solve quadratic equations) The two roots of a quadratic equation ax^2 + bx + c = 0 can be obtained using the following formula: b^2 - 4ac is ... May 30, 2023 ... The square root of the discriminant gives us (Edit: double?) the distance that each quadratic root lies either side of where the axis of symmetry crosses the x ... Jun 15, 2023 ... If the discriminant D < 0, then the quadratic equation ax 2 + bx + c = 0 will not have any real roots. Detailed step by step solution for k=(4ac-b^2)/(4a) F(z/Va- -b/2a) satisfies. (2) G(z)G(z + 1) = G(z2 + z - d), where d = (b2 - 4ac)/4a. The set Sd of roots of the polynomial G (z) is a finite nonempty set of ... 1. Let ƒ(x,y) = ax2 + bxy + cy2 be an indefinite binary quadratic form, with real coefficients a, b, c, and discriminant d = b2 —4ac.