If a,ß are the zeroes of px? – qx + r, then the value of a* +34 is?
Answers
Answered by
1
Answer:
Step-by-step explanation:
Given, x
4
+px
3
+qx
4
+rx+s=0
We know that,
∑a=a+b+c+d=−p…………….(1)
∑ab=ab+ac+ad+bc+bd+cd=q…………….(2)
∑abc=abc+abd+acd+bcd=−r…………….(3)
abcd=s…………….(4)
Squaring ∑ab, we get
(∑ab)
2
=(ab+ac+ad+bc+bd+cd)
2
⟹(∑ab)
2
=∑a
2
b
2
+2(a
2
bc+a
2
bd+a
2
cd+ab
2
c+ab
2
d+b
2
cd+abc
2
+ac
2
d+bc
2
d+abd
2
+acd
2
+bcd
2
)+6abcd
⟹(∑ab)
2
=∑a
2
b
2
+2∑a
2
bc+6abcd
⟹∑a
2
b
2
=(∑ab)
2
−2∑a
2
bc−6abcd…………….(5)
Now, Multiplying ∑a with ∑abc, we get
(a+b+c+d)(abc+abd+acd+bcd)=∑a
2
bc+4abcd
⟹∑a
2
bc=∑a∑abc−4abcd=(−p)⋅(−r)–4s=pr–4s
Substituting the value of ∑a
2
bc in (5), we get
∑a
2
b
2
=q
2
−2(pr−4s)–6s=q
2
–2pr+8s−6s=q
2
–2pr+2s
Similar questions