Question

The roots of the equation 2x^2-7x+5=0 are a and b without solving the roots find 1/a +1/b

Answer 1

$2x^{2} - 7x + 5 = 0$

By Vieta's relation we know the sum of the roots of this equation is -b/a and their product is c/a . Hence :

$a + b = 3.5\\\\ab = 2.5$

Dividing the first equation by the second :

$\frac{a+b}{ab} = \frac{3.5}{ab} \\\\ \frac{1}{a} +\frac{1}{b}= \frac{3.5}{2.5} \\ \\\frac{1}{a} +\frac{1}{b}= \frac{7}{5} \\\\\frac{1}{a} +\frac{1}{b} = 1.4$

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