# Polynomials

If b<0,and α,β are roots of the equation 2x^2 + 6x+b=0,and satisfy α/β + β/α<K.the the value of K?

Note by Abhishek Akella
4 years, 10 months ago

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$$\frac{\alpha}{\beta} + \frac{\beta}{\alpha} \\ = \frac{\alpha^2 + \beta^2}{\alpha\beta} \\ = \frac{ (\alpha + \beta)^2 - 2\alpha\beta}{\alpha\beta} \\ = \frac{ (\frac{-6}{2})^2}{\frac{b}{2}} - 2 \\ = \frac{18}{b} - 2 < -2 (as b < 0) \\ \Rightarrow k = \fbox{-2}$$

- 4 years, 10 months ago

(asb<0) wat does dis mean?

- 4 years, 10 months ago

I meant that $$\frac{18}{b} < 0$$ and hence $$\frac{18}{b} - 2 < -2$$

- 4 years, 10 months ago

kk thnxxx dude!!

- 4 years, 10 months ago