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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

Algebra

Roots of the nature

## Check the Answer

But try the problem first…

Answer: (c) $12$

Source

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 = $1 + 2 + 4 + 5 = 12$