How does the sign of -4ac affect the discriminant?

Jun 15, 2023 ... If the discriminant D < 0, then the quadratic equation ax 2 + bx + c = 0 will not have any real roots. Hence, the nature of the roots α and β of equation ax2 + bx + c = 0 depends on the quantity or expression (b2 – 4ac) under the square root sign. We say this ... We know that b2 - 4ac is the discriminant (D). Thus, the vertex formula is: (h, k) = (-b/2a, -D/4a) where D = b2 ... The expression under the radical in the quadratic formula is called the discriminant, i.e., D = b2 – 4ac · The nature of the roots of a quadratic equation can be ... -b 소. / b2 - 4ac. 2a . Step 2: Write your answer in the appropriate form: 1. If b2 - 4ac > 0, then there are two real roots r1 and r2 and the general ... The quadratic formula, x=- b±sqrt(b^2-4ac)/2a, can be derived by completing the square on the general standard form a quadratic equation. There will be at most two real solutions to any quadratic equation. The value of b2 − 4ac (known as the discriminant) tells us how many real solutions there are ... ... 2 + bxy + cy 2 of discriminant b 2 - 4ac = - d we can associate an ideal of norm a. Then the quadratic form associated to d with respect to this basis is Q ... Apr 7, 2014 ... I know how to derive the quadratic formula but not the alternate. -b ± √(b^2 - 4ac) b ± √(b^2 - 4ac) ... x1=(-b+sqrt(b^2-4ac))/2a=(-b+sqrt ... ... 2 + q, the graph of y = f(x) has a turning point at (−p, q). • For the quadratic equation ax2 + bx + c = 0, the expression b2 – 4ac is called the discriminant.