Try this beautiful problem Based on Quadratic equation, useful for ISI B.Stat Entrance.

Quadratic equation | ISI B.Stat Entrance | Problem 198


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

  • (a) \(18\)
  • (b) \(15)\)
  • (c) \(12\)
  • (d) None of these

Key Concepts


Quadratic equation

Algebra

Roots of the nature

Check the Answer


But try the problem first…

Answer: (c) \(12 \)

Source
Suggested Reading

TOMATO, Problem 198

Challenges and Thrills in Pre College Mathematics

Try with Hints


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 = \(1 + 2 + 4 + 5 = 12\)

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