Question

Sabendo que "K" satisfaz a equação {2(k-8) + 3(-k+1) = -4k +11} Os valores reais de x que satisfazem a equação 15x² - kx + 1 = 0 são:
A) 1/2 e 1/5
B) 1/2 e 2/5
C) 1/7 e 1/3
D) 1/5 e 1/3
E) 2/5 e 1/7

Answer 1

Answer:

D) 1/5 e 1/3

Step-by-step explanation:

You have the following quadratic equation:

$15x^2-kx+1=0$           (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:

$2(k-8)+3(-k+1)=-4k+11\\\\2k-16-3k+3=-4k+11\\\\2k-3k+4k=11+16-3\\\\3k=24\\\\k=8$

Next, you replace the previous value of k in the equation (1) and you use the quadratic formula to find the roots:

$15x^2-8x+1=0\\\\x_{1,2}=\frac{-(-8)\pm \sqrt{(-8)^2-4(15)(1)}}{2(15)}\\\\x_{1,2}=\frac{8\pm 2}{30}\\\\x_1=\frac{1}{5}\\\\x_2=\frac{1}{3}$

Then, the roots of the equation (1) are

D) 1/5 e 1/3