Answer:
D) 1/5 e 1/3
Step-by-step explanation:
You have the following quadratic equation:
[tex]15x^2-kx+1=0[/tex] (1)
In order to find the values of x that are solution to the equation (1), you first find the solution for k in the following equation:
[tex]2(k-8)+3(-k+1)=-4k+11\\\\2k-16-3k+3=-4k+11\\\\2k-3k+4k=11+16-3\\\\3k=24\\\\k=8[/tex]
Next, you replace the previous value of k in the equation (1) and you use the quadratic formula to find the roots:
[tex]15x^2-8x+1=0\\\\x_{1,2}=\frac{-(-8)\pm \sqrt{(-8)^2-4(15)(1)}}{2(15)}\\\\x_{1,2}=\frac{8\pm 2}{30}\\\\x_1=\frac{1}{5}\\\\x_2=\frac{1}{3}[/tex]
Then, the roots of the equation (1) are
D) 1/5 e 1/3
