Integral roots in quadratic equation The smallest possible natural number n,

kadetskihykw

kadetskihykw

Answered question

2022-04-24

Integral roots in quadratic equation
The smallest possible natural number n, for which the equation x2nx+2014=0 has integral roots, is
I know the discriminant will be a perfect square, but I am struck on equation of discriminant.

Answer & Explanation

Ann Mathis

Ann Mathis

Beginner2022-04-25Added 11 answers

The ' factorisation of 2014 is 2×19×53 is obviously a factor, so you need to find the factors of 1007 by hand. To do this, you only need to check the 's less than 100731.7 of which there aren't many.
This gives the factor pairs (1,2014);(2,1007);(19,106) and (38, 53). By Vieta's formulas, the sum of the two roots is ba in ax2+bx+c, or n1=n in your case. From here, you can immediately observe what the smallest value of n should be.

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