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

`k=(-11)/(2)`.

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=(1)/(2)`.

Lets use veita's formula.

By that formula we have the following equations:

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

`\alpha \cdot \beta=(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=(1)/(2)`, then
`k+6=(1)/(2)`.

Let's solve this for k:

Subtract 6 on both sides:

`k=(1)/(2)-6`

Find a common denominator:

`k=(1)/(2)-(12)/(2)`

Simplify:

`k=(-11)/(2)`.