Find the value of k such that the quadritic poly 3x square plus 2 kx plus x minus k minus 5 has the sum of zeroes as half of there product?

To find the value of k such that the quadratic polynomial has the sum of zeros as half of their product, we need to use the sum and product of zeros formula.

The sum of zeros formula states that for a quadratic equation of the form ax^2 + bx + c = 0, the sum of zeros is given by -b/a.

The product of zeros formula states that for the same quadratic equation, the product of zeros is given by c/a.

In this case, the quadratic polynomial is 3x^2 + 2kx + x - k - 5.

The sum of zeros is then -2k/3 and the product of zeros is -(-k-5)/3, which simplifies to (k+5)/3.

According to the given condition, the sum of zeros is half of the product of zeros. Mathematically, this can be written as:

(-2k/3) = 1/2 * ((k+5)/3)

To solve for k, let's simplify this equation step by step:

Multiply both sides of the equation by 3 to eliminate the denominators:

-2k = (k+5)/2

Multiply both sides of the equation by 2 to eliminate the fraction:

-4k = k+5

Combine like terms:

-4k - k = 5

-5k = 5

Divide both sides of the equation by -5:

k = -1

Therefore, the value of k that satisfies the given condition is -1.