Let be such that the equation has repeated root and if and are the roots of the equation , then is equal to:

Question

Let  be such that the equation  has repeated root  and if  and  are the roots of the equation , then  is equal to:

Canvas Classes · Accepted Answer

🧠 Repeated Root Forces  and  — Eliminate

If  is a repeated root of , then by Vieta:

So  and .

Now  and  are roots of . So  and .

From the second equation :  (using ).

Multiply by : , so .

This is the habit I want you to build. For "repeated root + another quadratic with the same root" problems: write the repeated-root condition explicitly via Vieta on the first quadratic, then plug into the second quadratic's Vieta sum/product to pin down the parameters.

🗺️ Working It Out

From first

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