# The sum of the roots 5x^2 - kx- 3 = 0 is equal to the products of the roots. Determine the value of k.

### 2 Answers | Add Yours

The quadratic equation may be determined if given the sum, `sum` , and the product, `prod` , of the roots.

`x^2- sum*x+prod=0`

Notice that the coefficient of x^2 of the given equation is 5, instead of 1, therefore divide the equation by 5.

`x^2-(k/5)*x-(3/5)=0`

Compare the equations and equate the coefficients.

`sum` `= k/5`

`prod` `= -3/5`

The problem asserts that `sum=prod ` =>`k/5=-3/5 =gt k=-3`

**ANSWER: k=-3**

Given the quadratic equation: 5x^2 - kx -3

==> a = 5 b= -k c = -3

Let x1 and x2 be the roots of the equation.

Then we know that:

==> x1 + x2 = -b/a = k/5

==> x1*x2 = c/a = -3/5

==> Bux1+x2 = x1*x2

==> k/5 = -3/5

==> k = -3

**Then the value of k is k= -3**