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Exercice 1 Résoudre dans R les inéquations suivantes : 2x^(2)-5x+3 > 0

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Exercice 1 Résoudre dans R les inéquations suivantes : 2x^(2)-5x+3 > 0

Exercice 1 Résoudre dans R les inéquations suivantes : 2x^(2)-5x+3 > 0

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ValerieMaster · Tutor for 5 years

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<p>1. \(x < \frac{1}{2}\) or \(x > 3\)</p>

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<p>1. To solve the quadratic inequality \(2x^2 - 5x + 3 > 0\), we can start by finding its roots. This requires factoring or using the quadratic formula:<br />\[x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\]<br />Where, for our equation:<br />a = 2, b = -5, and c = 3<br />Using the quadratic formula, the roots are:<br />\[x_1 = \frac{1}{2}\] and \[x_2 = 3\]<br />The quadratic curve, being positive (as a > 0), opens upwards. This means that the values of the quadratic will be negative between its roots and positive outside this interval.<br />Thus, the solution to the inequality \(2x^2 - 5x + 3 > 0\) is \(x < \frac{1}{2}\) or \(x > 3\).</p>
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