Question

Find a and b so that the polynomial, p(x)=x^2+ax-b passes through the points (6,-9) and (1, 16)

Answer 1

The given equation is:

p(x) = x^2 + ax - b

We write this in terms of y:

y = x^2 + ax – b

To solve for the values of the constants a and b, we are given the following conditions:

When x = 6, y = -9

When x = 1, y = 16

From these conditions, we can formulate two equation by substituting the values of y:

-9 = 6^2 + a(6) – b

6a = b – 45                           ---> 1

 

16 = 1^2 + a(1) – b

a = b + 15                             ---> 2

 

Combining equations 1 and 2:

6 (b + 15) = b – 45

6b + 90 = b – 45

5b = -135

b = -27

 

calculating for a using equation 1:

a = b + 15

a = -27 + 15

a = -12

 

Answers:

a = -12

b = -27