The sum of the roots 5x^2 - kx- 3 = 0 is equal to the products of the roots. Determine the value of k.
The quadratic equation may be determined if given the sum, `sum` , and the product, `prod` , of the roots.
Notice that the coefficient of x^2 of the given equation is 5, instead of 1, therefore divide the equation by 5.
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`
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