Question

If α, β are the zeros of the polynomial 3x2 + 5x - 7, then find 1/α + 1/β.​

Answer 1

Answer:

The answer is $\dfrac{5}{7}$

Step-by-step explanation:

Concept : If $\alpha,\beta$ are zeroes of $ax^2+bx+c$, then

                     $\alpha+\beta=-\dfrac{b}{a} \text{ and } \alpha\beta=\dfrac{c}{a}$

Here given $\alpha,\beta$ are the zeroes of $3x^2+5x-7$

              $\Rightarrow \alpha+\beta=-\dfrac{5}{3}, \alpha\beta=-\dfrac{7}3}$

Therefore  

             $\dfrac{1}{\alpha}+\dfrac{1}{\beta}=\dfrac{\beta+\alpha}{\alpha\beta}=\dfrac{-\frac{5}{3}}{-\frac{7}{3}}=\dfrac{5}{7}$