Question

please help me with 6 question

Answer 1

Heya !!!


( X + 1 ) and ( X - 2 ) are tow factor of the given polynomial.



X + 1 = 0 ----------X - 2 = 0


X = -1 ------------- X = 2

P(X) = X³ + AX² + 2X + B


P(-1) = (-1)³ + A × (-1)² + 2 × -1 + B



=> -1 + A × 1 - 2 + B = 0



=> -1 + A - 2 + B = 0



=> A + B = 3 --------(1)


And,


P(2) = (2)³ + A × (2)² + 2 × 2 + B = 0


=> 8 + A × 4 + 4 + B = 0



=> 4A + B = -12 ------(2)



From equation (1) we get,


A + B = 3



A = ( 3 - B ) -------(3)


Putting the value of A in equation (2)



4A + B = -12


4 × ( 3 - B ) + B = -12



12 - 4B + B = -12



-3B = -12 - 12


B = 24/3 = 8


Putting the value of B in equation (3)



A = 3 - B = 3 - 8 = -5



★ HOPE IT WILL HELP YOU ★