Question

pls answer my question I'll mark u brainlist if 1,-2,3 are the roots of x^3-bx^2+ax+6=0,then find a​

Answer 1

We have a = - 5, b = 2

Step-by-step explanation:

The given equation is

x³ - bx² + ax + 6 = 0 ..... (1)

Since 1, - 2, 3 are the roots of (1) no. equation,

1³ - b (1)² + a (1) + 6 = 0

or, 1 - b + a + 6 = 0

or, a - b + 7 = 0

or, b = a + 7 ..... (2)

(- 2)³ - b (- 2)² + a (- 2) + 6 = 0

or, - 8 - 4b - 2a + 6 = 0

or, a + 2b + 1 = 0

or, a + 2 (a + 7) + 1 = 0, by (2)

or, a + 2a + 14 + 1 = 0

or, 3a = - 15

or, a = - 5

∴ b = - 5 + 7 = 2, i.e., b = 2

3³ - b (3)² + a (3) + 6 = 0

or, 27 - 9b + 3a + 6 = 0

or, 3a - 9b + 33 = 0

or, a - 3b + 11 = 0, satisfied by a = - 5, b = 2

Therefore a = - 5, b = 2