Сатре о Find the condition that the roots of the quadratic equation
ax2 + cx + C =0
may be in the ratio m:n

Step-by-step explanation:

Given

Required

Condition that the roots is in m : n

Let the roots of the equation be represented as: mA and nA

A quadratic equation has the form:

or

We have the roots to be mA and nA.

So, the sum is represented as:

And the product is represented as:

By comparing:

with

So, we have:

Make A the subject:

Substitute

Multiply both sides by a

Cross Multiply:

Hence, the condition that the ratio is in m:n is

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step-by-step explanation: