The different in the roots of the equation 2x2 minus 11x 5 0 is ........

Quantitative Aptitude (CDS) Quadratic Equations

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The different in the roots of the equation 2x² −11x + 5 = 0 is

4.5

3.5

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Explanation:

Let $\alpha$ and $\beta$ be the root of this quadratic equation
2x² − 11x + 5 = 0
$\alpha + \beta = \frac{11}{2}$
$\alpha \beta = \frac{5}{2}$
We know that

$(\alpha- \beta)^{2} = (\alpha+ \beta)^{2}-4\alpha\beta =(\frac{11}{2})^{2}-4(\frac{5}{2})^{2}$
=> (11/2)² − 4 (5/2)
= (121/4) −(40/4)
=81/4= (9/2)²
Difference of roots = $(\alpha- \beta)=4.5$