19 Two zeroes of cubic polynomial ax +3x2-bx-6are-1 and -2. Find the t

1.	19 Two zeroes of cubic polynomial ax +3x2-bx-6are-1 and -2. Find the third zero and values ofaand b
Answer» ax³ + 3x² - bx - 6 x = -1 , -2 put the values of x in Equation we get, a(-1)³ + 3(-1)² - b(-1) - 6 = 0 => -a + 3 + b - 6 = 0 => b - a = 3--------(1) now x = - 2 a(- 2)³ + 3(-2)² - b(-2) - 6 = 0 => -8a + 12 + 2b - 6 = 0 => 2b - 8a + 6 = 0 => b - 4a = -3--------(2) from--(1) and -----(2) b - a = 3b - 4a = -3(-)___(+)__(+)———————3a = 6 => a = 2 put in --(1) b - 3 = 2 => b = 5 now put this value in Equation ax³ + 3x² - bx - 6 = 0 => 2x³ + 3x² - 5x - 6 = 0 two zeroes are given (-1 , -2) (x + 1)(x + 2) = x² + 2x + x + 2 = 0 => x² + 3x + 2 =0 x² + 3x + 2)2x³ + 3x² - 5x - 6(2x - 32x³ + 6x² + 4x- - -—————————-3x² - 9x - 6-3x² - 9x - 6+ + +—————————0 0 0 hence another zeroes is 2x - 3 = 0 => x = 3/2

19 Two zeroes of cubic polynomial ax +3x2-bx-6are-1 and -2. Find the third zero and values ofaand b

Answer»

ax³ + 3x² - bx - 6

x = -1 , -2

put the values of x in Equation

we get,

a(-1)³ + 3(-1)² - b(-1) - 6 = 0

=> -a + 3 + b - 6 = 0

=> b - a = 3--------(1)

now x = - 2

a(- 2)³ + 3(-2)² - b(-2) - 6 = 0

=> -8a + 12 + 2b - 6 = 0

=> 2b - 8a + 6 = 0

=> b - 4a = -3--------(2)

from--(1) and -----(2)

b - a = 3b - 4a = -3(-)___(+)__(+)———————3a = 6

=> a = 2 put in --(1)

b - 3 = 2

=> b = 5 now put this value in Equation

ax³ + 3x² - bx - 6 = 0

=> 2x³ + 3x² - 5x - 6 = 0

two zeroes are given (-1 , -2)

(x + 1)(x + 2) = x² + 2x + x + 2 = 0

=> x² + 3x + 2 =0

x² + 3x + 2)2x³ + 3x² - 5x - 6(2x - 32x³ + 6x² + 4x- - -—————————-3x² - 9x - 6-3x² - 9x - 6+ + +—————————0 0 0

hence another zeroes is

2x - 3 = 0

=> x = 3/2