What Is the Probability of No Real Roots in a Quadratic Equation?

Thread starter yuqiao
Start date Jan 27, 2010
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Probability

AI Thread Summary

The discussion centers on calculating the probability that the quadratic equation x^2 + ax + b = 0 has no real roots when a and b are randomly selected from the interval [0, 2]. The key condition for the equation to lack real roots is that the discriminant, given by a^2 - 4b, must be less than zero. Participants are encouraged to share their attempts and specific challenges to facilitate assistance. The conversation emphasizes collaborative problem-solving in understanding the mathematical concepts involved. Engaging with the problem can lead to a clearer grasp of quadratic equations and their properties.

Jan 27, 2010

yuqiao

Homework Statement

Given an interval [0,2], randomly select two numbers a, b in it. What is the probability of the situation where the equation x^2+ax+b=0 has no real root?

Homework Equations

The Attempt at a Solution

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Jan 27, 2010

tiny-tim

Science Advisor

Homework Helper

Hi yuqiao!

(try using the X² tag just above the Reply box

)

Show us what you've tried, and where you're stuck, and then we'll know how to help!

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