Try this beautiful problem Based on Quadratic equation, useful for ISI B.Stat Entrance.
Consider the quadratic equation of the form \(x^2 + bx + c = 0\). The number of such equations that have real roots and coefficients b and c from the set \(\{1, 2, 3, 4, 5\}\) (b and c may be equal) is
Quadratic equation
Algebra
Roots of the nature
But try the problem first...
Answer: (c) \(12 \)
TOMATO, Problem 198
Challenges and Thrills in Pre College Mathematics
First hint
The given equation is \(x^2 + bx + c = 0\).
we know that in the equation \(ax^2+bx+c=0\) ,the condition for real root is \(b^2-4ac \geq 0\)
Can you now finish the problem ..........
Final Step
Now, \(b^2 > 4c\)
b cannot be equal to 1.
If b = 2, c = 1
If b = 3, c = 1, 2
If b = 4, c = 1, 2, 3, 4
If b = 5, c = 1, 2, 3, 4, 5
Total number of equations = \(1 + 2 + 4 + 5 = 12\)
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
Try this beautiful problem Based on Quadratic equation, useful for ISI B.Stat Entrance.
Consider the quadratic equation of the form \(x^2 + bx + c = 0\). The number of such equations that have real roots and coefficients b and c from the set \(\{1, 2, 3, 4, 5\}\) (b and c may be equal) is
Quadratic equation
Algebra
Roots of the nature
But try the problem first...
Answer: (c) \(12 \)
TOMATO, Problem 198
Challenges and Thrills in Pre College Mathematics
First hint
The given equation is \(x^2 + bx + c = 0\).
we know that in the equation \(ax^2+bx+c=0\) ,the condition for real root is \(b^2-4ac \geq 0\)
Can you now finish the problem ..........
Final Step
Now, \(b^2 > 4c\)
b cannot be equal to 1.
If b = 2, c = 1
If b = 3, c = 1, 2
If b = 4, c = 1, 2, 3, 4
If b = 5, c = 1, 2, 3, 4, 5
Total number of equations = \(1 + 2 + 4 + 5 = 12\)
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
