We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
32
1
avatar+91 

Prove that if a quadratic has real coefficients such that the sum of the coefficients is zero, then the quadratic has real roots. 

 Jun 10, 2019
 #1
avatar+5172 
+4

\(\text{If $p(x)$ isn't monic, then normalize it so it is. $\\$This won't affect the roots or the sum of the coefficients being 0}\\ p(x) = x^2 + b x -(1+b)\\ p(x) = (x-1)(x+1+b) \text{ with roots}\\ x=1,~x=-(1+b) \text{, both of which are real}\)

.
 
 Jun 10, 2019
edited by Rom  Jun 10, 2019

10 Online Users