Question

if f(x)= ax²+bx+c, f(0)=2, f(1)=1, f(4)=c. find a,b,c​

Answer 1

Answer:

a= 2/3

b = -5/3

c = 2

here are your answer and please mark me as bra.inlie.st

Step-by-step explanation:

 

c= 2

sl.ving f(1)=1

a+b = -1=> (i)

slvin.g f(4)=6

4a+ b = 1=> (ii)

sol.ving => (i) and (ii)

we get

-3b = 5

b= -5/3

putting values of b and c in (i) , we get

a-5/3 = -1

a= 2/3

Answer 2

f(x) = ax²+bx+c

If, f(0)=2

So, a×(0)² + b×0 + c = 2

0 + 0 + c = 2

c = 2

If, f(1) = 1

So, a× 1² + b×1 + c = 1

a + b + c = 1

a + b + 2 = 1 (c = 2)

a + b = -1 ---------------eq(i)

If, f(4) = c

So, a × 4² + b×4 + c = c

16a + 4b = c - c

16a + 4b = 0

4 (4a + b) = 0

4a + b = 0 -------------eq(ii)

From eq(i), b = -1 -----------eq(iii)

Putting value of b from eq(iii) in eq(ii)

4a + (-1 -a) = 0

4a -1 -a = 0

3a = 1

a = 1/3

Putting value of a in eq(iii)

b = -1 -1/3

b = -4/3

Therefore,

Therefore,a = 1/3 , b = -4/3 & c = 2

• Hope it's helpful :)