Question

if alpha and beta are the zeros of polynomial 2 X square + X - 7 then the value of alpha + beta is ______

Answer 1

-1/2

Explanation:$\begin{gathered} \text{The polynomial }2Xsquare+X-7\colon \\ 2x^2\text{ + x - 7} \end{gathered}$

Since alpha and beta are zeros, thety are factors of the polynomial

$\begin{gathered} \text{for a quadratic function:} \\ ax^2\text{ - x(sum of factors)+ product of factors = 0} \end{gathered}$

$\begin{gathered} \text{Sum of factors} \\ \alpha\text{ + }\beta\text{ = }\frac{-b}{a} \\ \text{pro duct of factors:} \\ \alpha\text{ }\beta\text{ = c/a} \\ \end{gathered}$$\begin{gathered} a\text{ = 2, b = 1, c = -7} \\ su\text{ m = }\frac{-1}{2} \\ pr\text{ oduct = }\frac{-7}{2} \end{gathered}$$\begin{gathered} \text{The value of alpha +be ta = }\alpha+\text{ }\beta\text{ } \\ \alpha+\text{ }\beta\text{ }=\text{ -1/2} \end{gathered}$