Question

alpha and beta are the zeros of the polynomial x^2 -(k +6)x +2(2k -1). Find the value of k if alpha + beta = 1/2 alpha beta(ITS URGENT)

Answer 1

Answer:

$k=\frac{-11}{2}$.

Step-by-step explanation:

We are given $\alpha$ and $\beta$ are zeros of the polynomial $x^2-(k+6)x+2(2k-1)$.

We want to find the value of $k$ if $\alpha+\beta=\frac{1}{2}$.

Lets use veita's formula.

By that formula we have the following equations:

$\alpha+\beta=\frac{-(-(k+6))}{1}$  (-b/a where the quadratic is ax^2+bx+c)

$\alpha \cdot \beta=\frac{2(2k-1)}{1}$ (c/a)

Let's simplify those equations:

$\alpha+\beta=k+6$

$\alpha \cdot \beta=4k-2$

If $\alpha+\beta=k+6$ and $\alpha+\beta=\frac{1}{2}$, then $k+6=\frac{1}{2}$.

Let's solve this for k:

Subtract 6 on both sides:

$k=\frac{1}{2}-6$

Find a common denominator:

$k=\frac{1}{2}-\frac{12}{2}$

Simplify:

$k=\frac{-11}{2}$.