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Algebra Level 3

$x^2 + (2-p)x - p$

Let $a$ and $b$ be zeroes of the the polynomial above. Find the value of $p$ such that $a^2+b^2$ is minimized.

The answer is 1.

1 solution

Raj Rajput
Nov 3, 2015

Instead of differentiating $f(p)$ , we could find out the answer in this method: $\begin{aligned} f(p) &=p^2-2p+4 \\ &= (p-1)^2+3 \end{aligned}$ So, $f(p)$ will be minimum when, $p-1=0 \implies p=1$

Arpon Paul - 5 years, 7 months ago

I did same

Dev Sharma - 5 years, 7 months ago

Beautiful solution. .. and +1 and could you please tell how did you inserted image.

Rakshit Joshi - 5 years, 7 months ago

Thanks :) and for inserting any image, option is provided in bottom right corner :)

RAJ RAJPUT - 5 years, 7 months ago

All your problems have the same name.

Kushagra Sahni - 5 years, 7 months ago

My purpose in doing this was that everyone could recognise MY PROBLEMS .. and even names for algebra and number theory I have you know are different from geometry and likewise. But if you want then I may have different names for questions Kushagra.

Rakshit Joshi - 5 years, 7 months ago

@Rakshit Joshi – It depends entirely on you whether to change the name or not. I will have no problem because I liked all your problems till now and the question matters more than the name.

Kushagra Sahni - 5 years, 7 months ago

Do it here!

The answer is 1.

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