Kakatiya Academy Telangana SSC Class 10 Chapter 3

Class 10 • Chapter 3: Polynomials

Interactive polynomial visualiser • ax²+bx+c • Discriminant • Shape • Roots on graph

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Polynomial Visualiser

Move sliders for a, b, c. We'll redraw the parabola and explain the roots.

Opens Upward ↑

Real Roots

a (x²)

a = 1

b (x)

b = -5

c (constant)

c = 6

Equation

y = x² - 5x + 6

Discriminant • Roots • Nature

D = 1 (>0) Roots are real and distinct x₁ = 2 x₂ = 3

Red dots = x-intercepts (roots) if real.

What you are seeing Concept

1. a controls the 'opening': a>0 → U shape (opens upward), a<0 → ∩ shape (opens downward). 2. b and c move the graph left/right/up/down. 3. Discriminant D = b² - 4ac tells us about roots: • D > 0 → two different real roots. • D = 0 → one repeated real root (touches x-axis once). • D < 0 → no real roots (curve does not cross x-axis). 4. The red dots are where y = 0, i.e., the solutions of ax² + bx + c = 0.