find the condition that one root of x square + bx + c equal to zero maybe n times the other root
Answer (1)
17th Dec, 2020
Dear student,
The equation is given as :-
x^2 + bx + c = 0
Now, it is given that one root of the equation is n times the other root. So, let one of the root be k.
So, the other root will become nk.
Now sum of root = - coefficient of x / coefficient of x^2
Product of roots is = constant term / (coefficient of x^2)
Now,
Sum of root = nk+k = k(1+n) = -b /1
And product of root = (nk)k = nk^2 = c /1
From equation 1st, we have :-
k = -b/(1+n)
Substituting the value of k in equation 2nd we get :-
{(1+n)^2} / n = (b^2) / c
So, we got our final condition, if one of the root is n times the other.
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