Find a coefficient of quadratic polynomial, given the sum of its root.

Question

The sum of the zeros of $f(x) = x^2 − 3kx − 14$ is $3$. Find $k$.

How can I start this question?

Answer 1

The sum of zeros is the opposite of the coefficient of X, so that... $k$ is equal to $1$. Expand $(X-r_1)(X-r_2)$ to convince yourself.

Answer 2

Hint: Use Vieta's formulae.$$$$

Answer 3

let $x_1,x_2$ be the roots of equation $$ax^2+bx+c=0$$ from Viete formulas $$x_1+x_2=-b/a,x_1x_2=c/a$$ in your equation $a=1,b=-3k,c=-14$ then $$x_1+x_2=-(-3k)/1=3k$$ because $3k=3$ follow that $k=1$