Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Equations and Roots.
Consider the equation of the form \(x^{2}+bx+c=0\). The number of such equations that have real roots and have coefficients b and c in the set {1,2,3,4,5,6}, (b may be equal to c), is
Equation
Integers
Roots
Answer: 18.
B.Stat Objective Problem 123
Challenges and Thrills of Pre-College Mathematics by University Press
We know that if a quadratic equations have real roots then it's discriminant is >=0 so here \( b^{2}-4c \geq 0\). Now we will go casewise . First we will choose a particular Value for b then check what are the values of c that satisfies the above inequality.
for b=2, c=1
for b=3, c=1,2
for b=4, c=1,2,3,4
for b=5, c=1,2,3,4,5
for b=6, c=1,2,3,4,5,6
we get required number =18.
I.S.I. & C.M.I. Entrance Program
Taught by students and alumni of I.S.I. & C.M.I.
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
Cheenta students shine at the Purple Comet Math Meet 2025 organized by Titu Andreescu and Jonathan Kanewith top national and global ranks.
Celebrate the success of Cheenta students in the Stanford Math Tournament. The Unified Vectors team achieved Top 20 in the Team Round.
I think the answer given here is wrong. Please rectify it. The correct answer is 19.