Question

Find a quadrartic polynomial for which p(0)= -4, p(1)= -6 and p(2)= -4

Answer 1

Answer:

p(x) = 2x² - 4 - 4

Step-by-step explanation:

Let p(x) = ax² + bx + c

So, p(0) = a×0² + b×0 + c

        -4 = 0 + 0 + c

        c = -4

And, p(1) = a×1² + b×1 + c

     Put c = -4          

          -6 = a + b + (-4)

     a + b = -6 + 4 = -2

           a = -2 - b.........(1)

And, p(2) = a×2² + b×2 + c

      Put c = -4

           -4 = 4a + 2b + (-4)

  4a + 2b = -4 + 4

      Put a = -2 - b

  4(-2 - b) + 2b = 0

    -8 - 4b + 2b = 0

                  -2b = 8

                     b = -4

Put b = -4 in eq. (1)

      a = -2 - (-4)

      a = -2 + 4

      a = 2

So, p(x) = ax² + bx + c = 2x² - 4 - 4