Respuesta :

mhanifa

Answer:

  • k = -4 ± 2√5

Step-by-step explanation:

#22

Given

  • Equation x² -4x + 1 = k(x - 4) with equal roots

To find

  • The value of k

Solution

The equation in standard form is:

  • x² -4x + 1 = k(x - 4)
  • x² - 4x - kx + 1 + 4 = 0
  • x² - (k + 4)x + 5 = 0

When the quadratic equation has equal roots its discriminant is zero

  • D = 0
  • b² - 4ac = 0
  • (k + 4)² - 4*5 = 0
  • (k + 4)² = 20
  • k + 4 = ± √20
  • k = - 4 ± √20
  • or
  • k = -4 ± 2√5