SOLUTION: If the ratio of the roots of the equation x^2+bx+c=0 is as that of x^2+qx+r=0,then a)r^2b=qc^2 b)r^2c=qb^2 c)c^2r=q^2b d)b^2r=q^2c

Question 973011: If the ratio of the roots of the equation x^2+bx+c=0 is as that of x^2+qx+r=0,then
a)r^2b=qc^2
b)r^2c=qb^2
c)c^2r=q^2b
d)b^2r=q^2c
Answer by anand429(138) (Show Source): You can put this solution on YOUR website!
Let the roots of x^2+bx+c=0 be g and h, and
Let the roots of x^2+qx+r=0 be m and n
Let ratio of roots be given by g/h = R1 and m/n = R2
Now, g+h = -b ---(i)
and gh =c ---(ii)
Similarly,
m+n = -q ---(iii)
mn= r ----(iv)
Squaring eqn (i),

=> (using eqn. (ii)-----(v)
Divinding(v) by (ii)

=>
=>
Similarly,

Since R1=R2 (as per ques.),
So,
=>
=>
=>
Hence option (iv) is correct.

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