Show that the sum of the zeros product of the zeros and sum of the product of the zeros taken two at a time of the polynomial $2 x^{3} - 5 x^{2} - 14 x + 8$ are $\frac{5}{2}, - 4$ and $- 7$ respectively by finding the zeros of the polynomial.

Open in App

Solution

$\begin{matrix} α + β + λ = \frac{5}{2} (g i v e n) \Rightarrow α - β - λ = - 4 (g i v e n) a n d \Rightarrow α β + β λ + λ α = - 7 (g i v e n) \Rightarrow 2 x^{2} - 5 x^{2} - 14 x + 8 l e t r o o t s a r e α, β, a n d g l \Rightarrow s u m o f r o o t s (α + β + λ) = - \frac{(- 5)}{2} = \frac{5}{2} \Rightarrow p r o d u c t o f r o o t s (α β λ) = \frac{- d}{a} = \frac{- 8}{2} = 4 \Rightarrow s u m o f p r o d u c t o f r o o t s {(α + β + λ)}^{2} = \frac{c}{a} = \frac{- 14}{2} = 7 \end{matrix}$

Suggest Corrections

Similar questions

\frac{5}{2}, - 7, - 4

3, - 1

- 3

Join BYJU'S Learning Program