Further maths help needed!!!
Solve the equation 24x3+28x2-14x-3=0 given that the roots are a, a/r and ar
What I did was, I put the roots into brackets, so
(x-a)(x-a/r)(x-ar)
I expand this and put -a3 equal to -3, and get 1.44, although when I try to find r I get -0.049, -20.395 and -0.13 and -7.6
Can someone help me see where I have gone wrong?
What I did was, I put the roots into brackets, so
(x-a)(x-a/r)(x-ar)
I expand this and put -a3 equal to -3, and get 1.44, although when I try to find r I get -0.049, -20.395 and -0.13 and -7.6
Can someone help me see where I have gone wrong?
Original post by Juliakinga
Solve the equation 24x3+28x2-14x-3=0 given that the roots are a, a/r and ar
What I did was, I put the roots into brackets, so
(x-a)(x-a/r)(x-ar)
I expand this and put -a3 equal to -3, and get 1.44, although when I try to find r I get -0.049, -20.395 and -0.13 and -7.6
Can someone help me see where I have gone wrong?
What I did was, I put the roots into brackets, so
(x-a)(x-a/r)(x-ar)
I expand this and put -a3 equal to -3, and get 1.44, although when I try to find r I get -0.049, -20.395 and -0.13 and -7.6
Can someone help me see where I have gone wrong?
Can you post your working?
Original post by Muttley79
Can you post your working?
(X-a)(x-a/r)(x-ar)=
x3-arx2-ax2/r+a2x-ax2+a2rx+a2x/r-a2
-a3=-3
a=1.44
a2r+a2r2+a2=-14r
a2r+a2r2+a2+14r=0
2.0736r+2.0736r2+2.0736+14r=0
Put into quadratic equation.
r=-0.13
r=-7.6
I think what I did wrong was I didn't multiply the second equation by 24 so that the x3 values are equal
(edited 4 years ago)
Original post by Juliakinga
(X-a)(x-a/r)(x-ar)=
x3-arx2-ax2/r+a2x-ax2+a2rx+a2x/r-a2
I think what I did wrong was I didn't multiply the second equation by 24 so that the x3 values are equal
x3-arx2-ax2/r+a2x-ax2+a2rx+a2x/r-a2
I think what I did wrong was I didn't multiply the second equation by 24 so that the x3 values are equal
You need to see my second post ...
Original post by Muttley79
You need to see my second post ...
Yes thank you, I have just realised
use the fact that the product of the roots is equal to -(-3)/24 = 8. You can deduce that a=0.5. Now you can deduce that 1/r + 1 + r = -(28)/24*0.5 . Multiply by r since r cannot be zero to get a quadratic in r. Solve this. Find the 2 possibilities for 3 roots, and check which one satisfies that the sums of the pairs is equal to -14/24.
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