Question

If f(x) = ax^2 - bx - 1, f(2)=5. f(-2) = 10 find a, b.​

Answer 1

Answer:

a is 17/8

b is -5/4

Step-by-step explanation:

f(x) = ax² - bx - 1

f(2) = 5

a(2)² - b(2) - 1 = 5

4a - 2b = 5 + 1

4a - 2b = 6

2(2a + b) = 6

2a + b = 3

b = 3 - 2a   ----(1)

f(-2) = 10

a(-2)² + b(-2) - 1 = 10

4a - 2b = 10 + 1

4a - 2b = 11 ---(2)

put value if b in eq.--(2)

4a - 2(3 - 2a) = 11

4a - 6 + 4a = 11

8a = 11 + 6

8a = 17

a = 17/8

put value of a in eq.--(1)

b = 3 - 2(17/8)

b = 3 - 17/4

b = (12 - 17)/4

b = -5/4

Answer 2

Answer:

a = 5/4

b = 13/8

Step-by-step explanation:

f(2) = a(2)² – b(2) – 1

= a4 – b2 – 1

f(–2) = a(–2) – b(–2) – 1

= a4 + b2 – 1

f(2) = 5

a4 – b2 – 1 = 5

a4 = 6 + b2

a = 6 + b2/4

f(–2) = 10

a4 + b3 – 1 = 10

(6 + b2/4) (4) + b2 – 1 = 10

6 + b2 + b2 – 1 = 10

6 + b4 = 11 – 6

b = 5/4

f(2) = 5

a4 – b2 – 1 = 5

a4 – (5/4) (2) – 1 = 5

a4 – 5/2 = 4

a4 = 4 + 5/2

a4 = 13/2

a = 13/8