if alpha beta gamma are zeros of the polynomial x cube minus 12 x square + 44 X + c if two beta equals to Alpha Plus gamma, find the value of c
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☜☆☞hey friend!!! ☜☆☞
☆your answer is "c = -48"☆
Explaination ☆☆☞
________
Given ☞ x³-12x²+44x+c
let's alpha = P
.... beta = Q
Gama = R
then
P, Q, R roots and they are in AP
=> 2Q = P+R______(1)
from the equation we get
P+Q+R = 12______(2)
PQ + QR + RP = 44______(3)
PQR = -c_________(4)
substitute (1) in (2) we get
=> 2Q+Q = 12
=> 3Q = 12
=> Q = 4
=> P + R = 8________(5)
=> P×R = -c/4
substitute (5) in (2) we get
=> Q(P+R) + PR = 44
=> 4×8 - c/4 = 44
=> -c/4 = 12
=> c = -48________answer
hope it will help you
☆your answer is "c = -48"☆
Explaination ☆☆☞
________
Given ☞ x³-12x²+44x+c
let's alpha = P
.... beta = Q
Gama = R
then
P, Q, R roots and they are in AP
=> 2Q = P+R______(1)
from the equation we get
P+Q+R = 12______(2)
PQ + QR + RP = 44______(3)
PQR = -c_________(4)
substitute (1) in (2) we get
=> 2Q+Q = 12
=> 3Q = 12
=> Q = 4
=> P + R = 8________(5)
=> P×R = -c/4
substitute (5) in (2) we get
=> Q(P+R) + PR = 44
=> 4×8 - c/4 = 44
=> -c/4 = 12
=> c = -48________answer
hope it will help you
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