Try this beautiful problem from Algebra based Quadratic equation.
Both roots of the quadratic equation \(x^2 - 63x + k = 0\) are prime numbers. The number of possible values of \(k\) is
Algebra
Quadratic equation
prime numbers
Answer: \(1\)
AMC-10A (2002) Problem 12
Pre College Mathematics
The given equation is \(x^2 - 63x + k = 0\). Say that the roots are primes...
Comparing the equation with \(ax^2 +bx+c=0\) we get \(a=1 , b=-63 , c=k\).. Let \(m_1\) & \(m_2 \) be the roots of the given equation...
using vieta's Formula we may sat that...\(m_1 + m_2 =-(- 63)=63\) and \(m_1 m_2 = k\)
can you finish the problem........
Now the roots are prime. Sum of the two roots are \(63\) and product is \(k\)
Therefore one root must be \(2\) ,otherwise the sum would be even number
can you finish the problem........
So other root will be \(63-2\)=\(61\). Therefore product must be \(m_1m_2=122\)
Hence the answer is \(1\)
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
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.