Question

If f(x) = ax²-bx-1 , f (2)=5 , f (-2) =10
find a,b​

Answer 1

Step-by-step explanation:

when f ( 2 ) = 5

then,

f (2) = a(2)^2 - b ( 2 ) - 1

5 = 4a - 2b - 1

4a - 2b = 6

2 (2a - b ) = 6

2a - b = 3

a = 3 + b - - - 1.

when f (-2) = 10

f ( -2) = a ( -2 )^2 - b ( -2) -1

10 = 4a +2b -1

4a + 2b = 11

put 1 in this equation

we get 4 (3+b ) + 2b = 11

and then u can solve it

Answer 2

$f(x) = a {x}^{2} - bx - 1$

$f(2) = a {(2)}^{2} - b(2) - 1 = 5$

$4a - 2b - 1 = 5$

$4a - 2b = 6 \: \: \: \: ...(i)$

$f( - 2) = a {( - 2)}^{2} - b( - 2) - 1 = 10$

$f( - 2) = 4a + 2b - 1 = 10$

$4a + 2b = 11 \: \: \: \: ...(ii)$

Adding $(i)$ and $(ii)$

$8a = 17 \implies \boxed{a = \dfrac{17}{8} }$

Subtracting $(i)$ from $(ii)$

$4b = 5 \implies \boxed{ b = \dfrac{5}{4} }$