Quadratic Roots & Discriminant
Complex Numbers / Quadratic Equations · Class XI
Slide a, b, c of ax² + bx + c. Discriminant tells you real vs complex roots.
- Discriminant1
- Root 1 (real part)1.5
- Root 1 (imag part)0.5
- Sum of roots3
- Product of roots2
- y = a x² + b x + c
Formulas in this lab
- Discriminant
- Root 1 (real part)
- Root 1 (imag part)
- Sum of roots
- Product of roots
Frequently asked questions
▶What does the quadratic formula give you?
For $ax^2 + bx + c = 0$, the roots are $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. The discriminant $\Delta = b^2 - 4ac$ tells you the nature: $\Delta > 0$ two real, $\Delta = 0$ one repeated, $\Delta < 0$ two complex.
▶How do I use the quadratic roots lab?
Slide $a$, $b$ and $c$. The lab returns $\Delta$, both roots (real or complex), the sum of roots $-b/a$ and product of roots $c/a$. Try $a = 1$, $b = -3$, $c = 2$: roots are $1$ and $2$, sum $3$, product $2$.
▶Vieta's formulas: how do sum and product of roots help?
If $\alpha, \beta$ are roots, then $\alpha + \beta = -b/a$ and $\alpha\beta = c/a$. JEE problems often ask: form a quadratic whose roots are $1/\alpha, 1/\beta$ — use Vieta's, no need to solve. The lab shows both sum and product live so the link sinks in.
▶Where do quadratics show up in real life?
Projectile motion: a ball's height $h(t) = ut - \frac{1}{2}gt^2$ is a quadratic in time. Setting $h = 0$ gives the flight time via the quadratic formula. Maximising profit, optimising area for a given perimeter, and lens focal-length equations all reduce to quadratics.