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<title>11. Quadractic Quizzicality byhttps://blogs.warwick.ac.uk/jodielatham/entry/11_quadractic_quizzicality/2011-10-25T16:39:29Z2011-10-02T15:04:56Z<p><strong>11. Quadractic Quizzicality</strong></p>
<p><strong>Question: </strong>Suppose B and C are random numbers from a uniform(0,1) distribution. What is the probabilty that x^2 + Bx + C = 0 has two real roots?</p>
<p><strong>Solution:</strong> x has two real roots if its discriminant is greater than zero. i.e B^2 - 4C > 0. </p>
<p>So B^2 > 4C or c < B^2/4.</p>
<p>The sample space for B and C has an area of 1 and the area beneath the curve of C = B^2/4 represents the values for B and C that result in real roots.</p>
<p>So the probabilty that B^2 - 4C > 0 (the equation x^2 + Bx + C = 0 has two real roots) is the integral from 0 to 1 of B^2 /4 which is 1/12.<br />
</p><p><strong>11. Quadractic Quizzicality</strong></p>
<p><strong>Question: </strong>Suppose B and C are random numbers from a uniform(0,1) distribution. What is the probabilty that x^2 + Bx + C = 0 has two real roots?</p>
<p><strong>Solution:</strong> x has two real roots if its discriminant is greater than zero. i.e B^2 - 4C > 0. </p>
<p>So B^2 > 4C or c < B^2/4.</p>
<p>The sample space for B and C has an area of 1 and the area beneath the curve of C = B^2/4 represents the values for B and C that result in real roots.</p>
<p>So the probabilty that B^2 - 4C > 0 (the equation x^2 + Bx + C = 0 has two real roots) is the integral from 0 to 1 of B^2 /4 which is 1/12.<br />
</p>