Question 22

If $$ \alpha $$ & $$ \beta $$ are the zeros of the polynomial $$ 5 x^{2} -7x + 2 $$ then the sum of their reciprocals is:

Solution

The correct option is D

If the Quadratic equation is $$a^{2}$$+b$$x$$+ c = 0 then, 

$$\alpha$$ + $$\beta$$ = $$\frac{-b}{a}$$ = $$\frac{7}{5}$$

$$\alpha$$ $$\beta$$= $$\frac{c}{a}$$= $$\frac{2}{5}$$

$$\frac{1}{\alpha}$$ + $$\frac{1}{\beta}$$ = $$\frac{\alpha+\beta}{\alpha\beta}$$ 

  = $$\frac{\frac{7}{5}}{\frac{2}{5}}$$  = $$\frac{7}{2}$$


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