SOLUTION: Given that {{{a}}} and {{{ma}}} are the roots of the equation {{{x^2+px+q=0}}}, show that {{{mp^2 = (m+1)^2q}}}.

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Question 1146314: Given that and are the roots of the equation , show that .
Found 2 solutions by KMST, MathTherapy:
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
If thr roots of a quadratic equation are and ,
the equation can be written in factored form as
.
Doing the multiplication we find that
or
is the equivalent form of the quadratic equation,
in the form , with and .
Then,
, which simplifies to ,
which is obviously .

Answer by MathTherapy(10549)   (Show Source): You can put this solution on YOUR website!

Given that and are the roots of the equation , show that .
Since “a” and “ma” are roots of , then we can say that:
Sum of roots = a + ma
Also, sum of roots also =
Therefore, a + ma = - p
a(1 + m) = - p
------ eq (i)
Product of roots =
Product of roots also =
Therefore,
------ eq (ii)
-------- Substituting for a in eq (ii)

------- Cross-multiplying
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