Respuesta :

mhanifa

Answer:

  • a= -14/3
  • b= 11/3

Step-by-step explanation:

Given

  • Function h(x) = x^2 + ax + b
  • h(1) = 0
  • h'(1) = 4

To find

  • Values of a and b

Solution

h(1) = 0 ⇒

  • 1^2 + 1*a + b = 0 ⇒
  • a + b = -1      ------------------>   (1)

h'(1) = 4 ⇒ h(4) = 1 ⇒

  • 4^2 + 4*a + b = 1 ⇒
  • 4a + b = - 15   ------------------>  (2)

Considering the equation (1) in the equation (2)

  • 3a - 1 = -15
  • 3a = -14
  • a = - 14/3

and

  • b = -1 - a
  • b = -1 + 14/3  
  • b = 11/3

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