Question

समीकरण x³ + 3x² - 4x - 12 = 0को हल कीजिए

Answer 1

by taking common
x²(X+3)-4(X+3)
(x²-4)(X+3)

Answer 2

हल-

x³ + 3x² - 4x - 12 = 0

x = -2 इस समीकरण को संतुष्ट करता है क्योंकि

$( - 2) {}^{3} + 3 {( - 2)}^{2} - 4 \times ( - 2) - 12 = - 8 + 12 + 8 - 12 = 0 \\ \\ {x}^{3} + {2x}^{2} + {x}^{2} + 2x - 6x - 12 = 0 \\ \\ {x}^{2} (x + 2) + x(x + 2) - 6(x + 2) = 0 \\ \\ (x + 2)( {x}^{2} + x - 6) = 0 \\ \\ (x + 2)( {x}^{2} + 3x - 2x - 6) = 0 \\ \\ (x + 2)(x(x + 3) - 2(x + 3)) = 0 \\ \\ (x + 2)(x - 2)(x + 3) =0 \\ \\ x = - 2 \\ x = 2 \\ x = - 3$

अतः अभीष्ट हल 2,-2,-3