Question

if (x+1) and (x+2) are both factors of x^3+ax^2+bx-10 , find the values of a and bhelp !

Accepted Answer

As we have (x+1) (x+2) we can use substitution to solve and find the third factor. Remember that these factors are true when y or f(x) = 0
x^3+ax^2+bx-10 Substitute the two values you have (x=-1; x= -2)
f(-1)= (-1)^3 + a(-1)^2 + b(-1) - 10   
therefore 0= -1 +a - b - 10 multiply this line by 2. You'll see why later (b)  
therefore 0= -2 + 2a - 2b -20 Next use the other factor to create your second equation
f(-2) = (-2)^3 + a (-2)^2 + b(-2) - 10   
therefore 0 =-8 + 4a - 2b -10 
Now solve simultaneously:
(0=-2 +2a - 2b -20) - (0= -8 +4a -2b -10 )
The bs will cancel out  (which is why we multiplied earlier)and you will be left with
0= 6-2a -10
therefore 2a= -4
therefore a = -2
therefore y= x^3 -2x^2 + bx - 10 As these points are either turning points or intercepts y=0 and x = (-1) or you could use (-2)
therefore 0=(-1)^3 -2(-1)^2 + b(-1) - 10
0= -1 -2 -b -10
b= -13
therefore y= x^3-2x^2 -13x-10 
a=-2   b= -13

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if (x+1) and (x+2) are both factors of x^3+ax^2+bx-10 , find the values of a and b help !

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