Question

if the roots of the equation 3x^2+5x+2=0 are alpha and beta then what is the value of 1/alpha-1/beta . A)±1/2 , B)±1/3 , C)1/4 , D)5​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

3x²+5x+2=0

a=3

b=5

c=2

$root = \frac{ - b \binom{ +}{ - } \sqrt{ {b}^{2} - 4ac } }{2a}$

$\alpha = \frac{ - 5 + \sqrt{ {5}^{2} - 4 \times 3 \times 2 } }{2 \times 3} = \frac{ - 5 + \sqrt{25 - 24} }{6} = \frac{ - 5 + 1}{6} = \frac{ - 4}{6} = \frac{ - 2}{3}$

$\beta = \frac{ - 5 - \sqrt{ {5}^{2} - 4 \times 3 \times 2} }{2 \times 3} = \frac{ - 5 - \sqrt{25 - 24} }{6} = \frac{ - 5 - 1}{6} = \frac{ - 6}{6} = - 1$

$\frac{1}{ \alpha } - \frac{1}{ \beta } = \frac{ - 3}{2} - ( - 1) = \frac{ - 3 + 2}{2} = \frac{ - 1}{2}$