Find the values of a and b so that the expression x³
+ 10x² + ax + b is exactly divisible by x - 1 as well
as x -2.
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x³ + 10x² + ax + b
x - 1 = 0 then x = 1
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1³ + 10(1²) + a(1) + b = 0
1+10+a+b = 0
11 + a + b = 0
a + b = -11 → eq - 1
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( x - 2 = 0) ; x = 2
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2³ + 10(2²) + a(2) + b = 0
8 + 40 + 2a + b = 0
48 + 2a + b = 0
2a + b = -48 → eq - 2
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subtract eq - 1 from eq - 2
2a + b = -48
a + b = -11
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a = -37
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substitute a value in eq - 1
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a + b = -11
-37 + b = -11
b = -11 + 37
b = 26
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a = -37 ; b = 26
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I hope this answer helps you
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