Answer:
k = - 6 , c = 8
Explanation:
f(x) = x² + kx + c
given f(2) = 0 , substitute (2, 0 ) into f(x)
0 = 2² + 2k + c
0 = 4 + 2k + c ( subtract 4 from both sides )
- 4 = 2k + c → (1)
given f(- 3) = 35 , substitute (- 3, 35 ) into f(x)
35 = (- 3)² - 3k + c
35 = 9 - 3k + c ( subtract 9 from both sides )
26 = - 3k + c → (2)
subtract (2) from (1) term by term to eliminate c
- 4 - 26 = 2k - (- 3k) + (c - c)
- 30 = 2k + 3k
- 30 = 5k ( divide both sides by 5 )
- 6 = k
substitute k = - 6 into (1) and solve for c
- 4 = 2(- 6) + c
- 4 = - 12 + c ( add 12 to both sides )
8 = c
then
k = - 6 and c = 8