Construct a polynomial function of least degree possible using the given information.
1 answer:
Answer:
f(x) = (-5/3)x³ +5x² +(5/3)x -5
Step-by-step explanation:
For root "a", the polynomial will have a factor (x -a). Given the three roots, the polynomial will be the product of the three factors ...
... p(x) = (x +1)(x -1)(x -3)
The value of p(2) is 3·1·(-1) = -3. In order to make f(2) = 5, we need to multiply p(x) by -5/3.
... f(x) = (-5/3)p(x)
... f(x) = (-5/3)(x +1)(x -1)(x -3)
Expanding gives
... f(x) = (-5/3)x³ +5x² +(5/3)x -5
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Answer:
a) Each 1m² of fence panel costs: £2
b) I metre of wooden frame costs: £1
Step-by-step explanation:
Let the price of 1 sq.m. of fence panel be x
Let the price of 1 m of wooden frame be y
In Fig 1
Length = 4 m
Breadth = 3 m
Area =
Cost of 1 sq.m. = x
Cost of 12 sq.m. = 12x
Perimeter =2(l+b)=2(4+3)=14 m
Cost of 1 m of wooden frame = y
Cost of 14 m of wooden frame = 14y
We are given that total cost of framing and fencing is 38
So. 12x+14y=38 ----1
In Fig 2
Length = 6 m
Breadth = 2 m
Area =.
Cost of 1 sq.m. = x
Cost of 12 sq.m. = 12x
Perimeter =2(l+b)=2(6+2)=16 m
Cost of 1 m of wooden frame = y
Cost of 16 m of wooden frame = 16y
We are given that total cost of framing and fencing is 40
So. 12x+16y=40---2
Substitute the value of 12x form 1 in 2
38-14y+16y=40
2y=2
y=1
Substitute the value of y in 2
12x+16=40
12x=24
x=2
So, cost of 1 sq.m. of fence panel is 2 and cost of 1 m of wooden frame is 1
In fig 3
To verify :
Length = 3 m
Breadth = 5 m
Area =
Cost of 1 sq.m. = 2
Cost of 12 sq.m. =
Perimeter =2(l+b)=2(3+5)=16 m
Cost of 1 m of wooden frame = 1
Cost of 16 m of wooden frame = 16
So, Total cost = 30+16=46
We are given that cost of fencing and framing is 46
Thus verified
Hence
a) Each 1m² of fence panel costs: £2
b) I metre of wooden frame costs: £1