Question 116
If the equation $$2x^{2}-7x+12=0$$ has two roots $$\alpha$$ and $$\beta$$ then the value of $$\frac{\alpha}{\beta}$$+$$\frac{\beta}{\alpha}$$ is
Solution
Equation : $$2x^{2}-7x+12=0$$
=> Sum of roots = $$\alpha + \beta = \frac{7}{2}$$
=> Product of roots = $$\alpha \beta = \frac{12}{2} = 6$$
To find : $$\frac{\alpha}{\beta}$$+$$\frac{\beta}{\alpha}$$
= $$\frac{\alpha^2 + \beta^2}{\alpha \beta}$$
= $$\frac{(\alpha + \beta)^2 - 2 \alpha\beta}{\alpha \beta}$$
= $$\frac{\frac{49}{4} - 12}{6}$$
= $$\frac{\frac{1}{4}}{6} = \frac{1}{24}$$
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