This is the equation I need to find it for:
X^4 - 17x^3 - 24x^2 + 310
Your help is greatly appreciated :D
X^4 - 17x^3 - 24x^2 + 310
Your help is greatly appreciated :D
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x^4 - 17x^3 - 24x^2 + 310
Assuming this has got roots a b c d then
(x - a)(x - b)(x - c)(x - d)
= x^4-(a + b + c + d)x^3 + (ab + ac + ad + bc + bd + cd)x^2 + ... (other terns not required)
from above
a + b + c + d = 17 (comparing coefficients)
now ab + ac + ad + bc + bd + cd = - 24
(a + b + c + d)^2 = a^2 + b^2 + c^2 + d^2 + 2(ab + ac + ad + bc + bd + cd)
or 17^2 = a^2 + b^2 + c^2 + d^ - 2 * 24
or a^2 + b^2 + c^2 + d^2 = 17^2 + 2*24 = 289 + 48 or 337
so sum = 17
sum of squares of roots = 337
Assuming this has got roots a b c d then
(x - a)(x - b)(x - c)(x - d)
= x^4-(a + b + c + d)x^3 + (ab + ac + ad + bc + bd + cd)x^2 + ... (other terns not required)
from above
a + b + c + d = 17 (comparing coefficients)
now ab + ac + ad + bc + bd + cd = - 24
(a + b + c + d)^2 = a^2 + b^2 + c^2 + d^2 + 2(ab + ac + ad + bc + bd + cd)
or 17^2 = a^2 + b^2 + c^2 + d^ - 2 * 24
or a^2 + b^2 + c^2 + d^2 = 17^2 + 2*24 = 289 + 48 or 337
so sum = 17
sum of squares of roots = 337
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ANSWER: SUM OF SQUARES OF ROOTS = 556.98
Why??
Roots: (approx) 2.155, -3.658, 4.122 and -14.879
AVERAGE OF ROOTS = -12.259
SUM OF SQUARES OF ROOTS = (2.155 +12.259)² + (-3.658 -12.259)² + (4.122 -12.259)² +
(-14.879 -12.259)² = 556.98
Why??
Roots: (approx) 2.155, -3.658, 4.122 and -14.879
AVERAGE OF ROOTS = -12.259
SUM OF SQUARES OF ROOTS = (2.155 +12.259)² + (-3.658 -12.259)² + (4.122 -12.259)² +
(-14.879 -12.259)² = 556.98
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Let x1, x2, x3, x4 be the real or complex roots of x^4 - 17x^3 - 24x^2 + 310.
Then
x^4 - 17x^3 - 24x^2 + 310 = (x - x1)(x - x2)(x - x3)(x - x4) =
................ .................. . = x^4 - (x1 + x2 + x3 + x4)x^3 + (x1x2 + x1x3 + ...)x^2 + ...
hence
x1 + x2 + x3 + x4 = 17
x1x2 + x1x3 + x1x4 + x2x3 + x2x4 + x3x4 = -24
x1^2 + x2^2 +x3^2+x4^2 = (x1+x2+x3+x4)^2 - 2(x1x2 + ... + x3x4) = 17^2 - 2(-24) = 337
bye
Then
x^4 - 17x^3 - 24x^2 + 310 = (x - x1)(x - x2)(x - x3)(x - x4) =
................ .................. . = x^4 - (x1 + x2 + x3 + x4)x^3 + (x1x2 + x1x3 + ...)x^2 + ...
hence
x1 + x2 + x3 + x4 = 17
x1x2 + x1x3 + x1x4 + x2x3 + x2x4 + x3x4 = -24
x1^2 + x2^2 +x3^2+x4^2 = (x1+x2+x3+x4)^2 - 2(x1x2 + ... + x3x4) = 17^2 - 2(-24) = 337
bye
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Islands of adventure (a day with my boyfriend) a few questions ! plz help !?
ok so yesturday there was a school field trip and i spent it with my new boyfriend. (we've only been going out for 3 days). the fieldtrip was to islands of adventure and it wasnt just me and my boyfriend... it was us and a group of friends but i was mostly with him. we kissed a few times, hugged , held hands, he hugged me from behind and stuff, like normal couples do. (im in 8th grade). as we were waiting in line, he hugged me from behind and i noticed he gave me a kiss on the top of my head, this happend many times troughout the day and i jst wondered what it ment. later on when we went to eat, we had to exit the park using a little entrance ticket. since i got on a water ride and the ticket was in my pocket , the ticket was destroyed and faded. when we were finished eating we arrived at the entrance again and when i tried to scan the ticket, the employee said i had to wait in line at guest services to get a new ticket. i told my group of friends, (including my boyfriend) to plz wait for me because i didnt have my phone to contact them, so they waited about 15 minutes. when i finally got my new ticket, my boyfriend was the ONLY one waiting for me> i felt very flattered that he will wait so long (almost an hour) in the blazing sun. i felt so guilty at the same time but he kept assuring me everything was ok and stuff. so i walked with him till i met up with the group an i met up with my bestfriend and decided to ride a ride with her since i didnt spend any time with her the whole time i was there . so my boyfriend went along with the group. ( i didnt mean to ditch him like that, i felt very bad afterwards) i got my phone while i was in line (my friend had it) and i texted him ad he said he misses me. after that ride i met up with him by the lockers and he pulled me to a corner and gave me an engraved bracelet with our names and our date on it. i thought it was sooooooo sweeet to i gave him a kiss. after this we spent the rest of the day together. all im trying to figure out is (does he really like me?) does the kiss on the head or the bracelt mean anything)?
Islands of adventure (a day with my boyfriend) a few questions ! plz help !?
ok so yesturday there was a school field trip and i spent it with my new boyfriend. (we've only been going out for 3 days). the fieldtrip was to islands of adventure and it wasnt just me and my boyfriend... it was us and a group of friends but i was mostly with him. we kissed a few times, hugged , held hands, he hugged me from behind and stuff, like normal couples do. (im in 8th grade). as we were waiting in line, he hugged me from behind and i noticed he gave me a kiss on the top of my head, this happend many times troughout the day and i jst wondered what it ment. later on when we went to eat, we had to exit the park using a little entrance ticket. since i got on a water ride and the ticket was in my pocket , the ticket was destroyed and faded. when we were finished eating we arrived at the entrance again and when i tried to scan the ticket, the employee said i had to wait in line at guest services to get a new ticket. i told my group of friends, (including my boyfriend) to plz wait for me because i didnt have my phone to contact them, so they waited about 15 minutes. when i finally got my new ticket, my boyfriend was the ONLY one waiting for me> i felt very flattered that he will wait so long (almost an hour) in the blazing sun. i felt so guilty at the same time but he kept assuring me everything was ok and stuff. so i walked with him till i met up with the group an i met up with my bestfriend and decided to ride a ride with her since i didnt spend any time with her the whole time i was there . so my boyfriend went along with the group. ( i didnt mean to ditch him like that, i felt very bad afterwards) i got my phone while i was in line (my friend had it) and i texted him ad he said he misses me. after that ride i met up with him by the lockers and he pulled me to a corner and gave me an engraved bracelet with our names and our date on it. i thought it was sooooooo sweeet to i gave him a kiss. after this we spent the rest of the day together. all im trying to figure out is (does he really like me?) does the kiss on the head or the bracelt mean anything)?