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Grade 10Algebra

i have 2 questions ---
  1. The Condition that the roots of the eqn ax2 + bx + c = 0 such that one root is n times the other is :
a) na2= bc(n+1)2
b) nb2= ca (n+1)2
c) nc2=ab(n+1)2
2. the root of the eqn ax2+bx+c = 0 are in the ratio m:n, then
a)mna2=(m+n)c2
b)mnb2=(m+n)ac
c)mnb2=(m+n)2ac

Profile image of Ashwin
11 Years agoGrade 10
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1 Answer

Profile image of SHAIK AASIF AHAMED
ApprovedApproved Tutor Answer11 Years ago
Hello student,
Please find the answer to your question below
1)let the roots be x,xn
so x+xn=(-b/a) and x2n=c/a
x=(-b/a(n+1)).........(1) and also x2=(c/an).......(2)
substituting 1 in 2 we get
nb2= ca (n+1)2
2)let (x/y)=(m/n)
So km,kn are roots of ax2+bx+c=0
so k(m+n)=-b/a and
k2mn=c/a
so (m+n)2/mn=(b/a)2+(c/a)
So mnb2=(m+n)2ac