Question

If x^3+ax^2-bx+10 is divisible by x^2-3x+2 find the value of a and b.

Answer 1

★ QUADRATIC RESOLUTION ★

Given cubic equation :

x^3 + ax² - bx + 10=0 is divisible by x² - 3x + 2 = 0

x² - 3x + 2 = 0 [ Resolving in factors ]

x² - 2x - 1x + 2 = 0

x ( x - 2 ) - 1 ( x - 2 ) = 0

x - 1 ( x - 2 ) = 0

Hence , x = 1 , 2

Therefore , the cubic equation will also be satisfied by x = 1 , 2

By substituting x = 1

a - b = - 11

By substituting x = 2

2a - b = -9

Hence , solving the given two linear equivalents

2a - 2b = -22 and 2a - b = -9

b = -13 and substituting the value of b in earlier equations , we get the value of " a "

Hence ,

a = 2 and b = -13

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Answer 2

Answer:

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Step-by-step explanation:

★ QUADRATIC RESOLUTION ★

Given cubic equation :

x^3 + ax² - bx + 10=0 is divisible by x² - 3x + 2 = 0

x² - 3x + 2 = 0 [ Resolving in factors ]

x² - 2x - 1x + 2 = 0

x ( x - 2 ) - 1 ( x - 2 ) = 0

x - 1 ( x - 2 ) = 0

Hence , x = 1 , 2

Therefore , the cubic equation will also be satisfied by x = 1 , 2

By substituting x = 1

a - b = - 11

By substituting x = 2

2a - b = -9

Hence , solving the given two linear equivalents

2a - 2b = -22 and 2a - b = -9

b = -13 and substituting the value of b in earlier equations , we get the value of " a "

Hence ,

a = 2 and b = -13