Prime???

x ² 63 x + k = 0 x²-63x+k=0

This equation has two prime zeros. What is the product of them?


The answer is 122.

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3 solutions

Joshua Lowrance
Sep 25, 2019

( x p 1 ) ( x p 2 ) = x 2 p 1 x p 2 x + p 1 p 2 = x 2 ( p 1 + p 2 ) x + p 1 p 2 (x-p_1)(x-p_2) = x^2-p_1x-p_2x+p_1p_2=x^2-(p_1+p_2)x+p_1p_2 (where p 1 p_1 and p 2 p_2 are the two prime zeros of the function)

So we know that p 1 + p 2 = 63 p_1+p_2=63 , and p 1 p 2 = k p_1p_2=k . Because 63 63 is odd, the only two primes that can add together to get 63 63 are 2 2 and 61 61 . The product of these two primes is 2 × 61 = 122 2\times61=122 .

Hey Lawrence, how can I add a picture in my problem

arifin ikram - 1 year, 8 months ago

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When you are editing you post, there is a toolbar at the top of the text box. The third one from the left should be the image (there is an icon depicting a photo). Click that, and you can upload the photo you want.

Joshua Lowrance - 1 year, 8 months ago
Arifin Ikram
Sep 25, 2019

This equation has two prime zeros and k us not given. So 63 can be devide into two primes. 63 is a odd number. Obviously 2 is one of them. And the other is 63-2=61 .

So our answer will be 61 × 2 = 122 \boxed {61\times2=122}

Zhong Si Wei
Sep 26, 2019

By vieta's formula, Sum of the roots/ zeroes : 63/1 = 63 The only possible combination of prime numbers is 2 and 61. So product of zeroes : 122

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