Question

Determina el valor que debe tener K en la siguiente ecuación: (K 2) x 2 (5K 2)x 3K 1 = 0, para que la suma de sus raíces sea 6.

Answer 1

Respuesta:

(K + 2) x² + (5k + 2) x + 3k +1 = 0

X1 = -b + √b² - 4ac / 2a

X2 = -b - √b² - 4ac / 2a

X1 + x2 = -b + √b² - 4ac / 2a + -b + -b - √b² - 4ac / 2a

X1 + x2 = -2ab / 2a = X1 + x2 = -b / a

X1 + x2 = 6  

-b / a = 6

- (5k + 2) / k + 2 = 6

-5k -2 = 6(k + 2)  

-5k -2 = 6k +12

-11k = 14

K = -14 / 11

(k + 2) x² + (5k + 2) x + 3k +1 = 0

(-14 / 11 + 2) x² + (5 * -14 / 11 + 2) x + 3 * -14 / 11 + 1 = 0

8x² - 48x – 31 = 0

V = (h, k)

H = -b / 2a = -(-48) / 2(8) = 3

K = f (h) = f (3) = 8 (3)² - 48(3) – 31 = 0

F (3) = -103

V = (h, k) = (3, - 103)  

Intercepto con el eje ‘’x’’:

Y = 0  

F(x) = 0  

8x² - 48x – 31 = 0

X1 = 6.59  

X2 = 0,58  

(x, y) =  (6. 59, 0)

(x, y) = (-0. 58, 0)

V = (3, - 103)  

K= -14/11  

Explicación: