Question

If α and β are roots of quadratic equation 2 x2

- 10 x + 5 = 0 the value of 1
/α
+

1
/β
is​

Answer 1

Answer: The answer is given in the attachment

Answer 2

$Given \:\alpha \: and \: \beta \:are \: roots \:of$

$a \: Quadratic \: equation \: 2x^{2}-10x+5=0$

$i) Sum \:of \: the \:roots = \frac{Coefficient \:of \: x }{Coefficient \:of \: x^{2}}$

$\implies \alpha + \beta = \frac{-(-10)}{2}$

$= \frac{10}{2}$

$= 5 \: --(1)$

$ii) Product\:of \: the \:roots = \frac{Constant \:term}{Coefficient \:of \: x^{2}}$

$\implies \alpha \beta = \frac{5}{2}$

$= \frac{5}{2}\: ---(2)$

$\red{ Value \: of \: \frac{1}{\alpha} + \frac{1}{\beta}}$

$= \frac{\beta + \alpha }{\alpha \beta }$

$= \frac{ 5}{\frac{5}{2}}$

$= 5 \times \frac{2}{5}$

$= 2$

Therefore.,

$\red{ Value \: of \: \frac{1}{\alpha} + \frac{1}{\beta}} \green { = 2 }$

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