Question

this is from lesson 2 of maths of class 9th please solve it​

Answer 1

Answer:

        a = 22/19  and  b = 708/19

Step-by-step explanation:

     x⁴ + ax³ - 7x² + 8x + b is divisible by x+2

⇒  (-2)⁴ + a×(-2)³ - 7×(-2)² + 8×(-2) + b  =  0, by the Factor Theorem

⇒  16 - 8a - 28 - 16 + b  =  0

⇒  -8a + b  =  28      ...(1)

     x⁴ + ax³ - 7x² + 8x + b is divisible by x+3

⇒  (-3)⁴ + a×(-3)³ - 7×(-3)² + 8×(-3) + b  =  0, by the Factor Theorem

⇒  81 - 27a - 63 - 24 + b  =  0

⇒  -27a + b  =  6      ...(2)

Subtracting equation (2) from equation (1) gives

    -8a + 27a  =  28 - 6

⇒  19a = 22

⇒  a = 22/19

Substituting into (1) gives

   b  =  28 + 8a  =  28 + 8×22/19  = 708/19