Homework Help

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

user profile pic

alina6578 | Student, Grade 9 | eNotes Newbie

Posted November 20, 2011 at 7:10 AM via web

dislike 0 like

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

user profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted November 20, 2011 at 7:22 AM (Answer #1)

dislike 0 like

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

 

 

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted November 22, 2011 at 6:46 PM (Answer #2)

dislike 0 like

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

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes