Quadratic Formula ಅನ್ನು ಹೇಗೆ ಲೆಕ್ಕ ಹಾಕುವುದು
Quadratic Formula ಎಂದರೇನು?
The quadratic formula solves any equation of the form ax² + bx + c = 0 for x. It works for all quadratics — even ones that cannot be factored — making it the most universal solving method. The formula was known to Babylonian mathematicians as early as 2000 BC.
ಹಂತ-ಹಂತದ ಮಾರ್ಗದರ್ಶಿ
- 1Arrange the equation in standard form: ax² + bx + c = 0
- 2Identify a (coefficient of x²), b (coefficient of x), c (constant)
- 3Calculate the discriminant: Δ = b² − 4ac
- 4If Δ ≥ 0: substitute into x = (−b ± √Δ) / 2a for two real roots
- 5If Δ < 0: the equation has two complex (non-real) roots
Worked Examples
ಇನ್ಪುಟ್
x² − 5x + 6 = 0
ಫಲಿತಾಂಶ
x = 3 or x = 2
Δ = 25−24 = 1 > 0. Roots: (5±1)/2
ಇನ್ಪುಟ್
x² − 2x + 1 = 0
ಫಲಿತಾಂಶ
x = 1 (repeated)
Δ = 4−4 = 0. One repeated root.
ಇನ್ಪುಟ್
x² + x + 1 = 0
ಫಲಿತಾಂಶ
Complex roots
Δ = 1−4 = −3 < 0. No real solutions.
ಇನ್ಪುಟ್
2x² + 3x − 2 = 0
ಫಲಿತಾಂಶ
x = 0.5 or x = −2
Δ = 9+16 = 25. Roots: (−3±5)/4
ಲೆಕ್ಕಾಚಾರ ಮಾಡಲು ಸಿದ್ಧರಿದ್ದೀರಾ? ಉಚಿತ Quadratic Formula ಕ್ಯಾಲ್ಕುಲೇಟರ್ ಅನ್ನು ಪ್ರಯತ್ನಿಸಿ
ನೀವೇ ಪ್ರಯತ್ನಿಸಿ →