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f(x) = x^3 + ax^2 + bx + 3. given that when f(x) is divided by (x + 2) the remainder is 7, show that 2a - b = 6 |
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Answer» Answer: So a=3 and b=8 Step-by-step explanation: f(x)=2X 3 +ax −bx+3 At x=2 f(2)=15 f(1)=0 f(x)=2x 3 +ax 2 −bx+3 f(1)= 2+a-b+3=0 a-b+5=0......A f(x)= 2x 3 +ax 2 −bx+3 f(2)=2(2 3 )+a(2 2 )−2b+3=15 4a-2b=-4 Multiply A by 2 and subtract from above EQUATION 4a-2b=-4 2a-2b+10=0 2a-10=-4 2a= 6 a=3 From A 3-b+5=0 8-b=0 b=8 So a=3 and b=8 |
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