.If the roots of the quadratic equation p (q - r) x + q (r − p) x + r (p − q) = 0 are real and equal , show that - + . = / .
Answers
Answered by
0
Answer:
p(q−r)x
2
+q(r−p)x+r(p−q)=0
D=0∴ the root are equal
D=b
2
−4ac
⇒(q(r−p))
2
−4(p(q−r))(r(p−q)))=0
⇒q
2
(r
2
+p
2
−2pr)−4((pq−pr)(pr−qr))=0
⇒q
2
(r
2
+p
2
−2pr)−4(p
2
qr−pq
2
r−p
2
r
2
+pqr
2
)=0
⇒q
2
r
2
+p
2
q
2
−2pq
2
r−4p
2
qr+4pq
2
r+4p
2
r
2
+4pqr
2
=0
⇒q
2
r
2
+p
2
q
2
+4p
2
r
2
−4p
2
qr+2pq
2
r+4pqr
2
=0
⇒(pq+qr−2pr)
2
=0[∵(a+b+c)
2
=a
2
+b
2
+c
2
−2ab+2bc+2ac]
⇒pq+qr=2pr
Dividing by p=qr
r
1
+
p
1
=
q
2
Hence , m=2
Similar questions