Question

Moderm packaging plays an important role in modern industry. There are more than
60,000 scientists conducting research related to packaging engineering. In the last few
decades, the packaging materials and packaging logistics have been rapidly developed
that brought new challenges to mathematic modeling and simulation. For the box to
satisfy certain requirements its length must be 3m greater than the width and
its
height must be 2m less than the width.
i) If width is taken as X units, which of the following polynomial represents the
volume of the box?
Cx+6x-6x
B)x+3x
A) x- 5x-6
D)x+x -6
ii) Which of the following polynomial represents the area of paper used to make
the base of the box?
C)x'+6x-6x
A) x-5x-6
B) 6x +4x- 12
D) 6x+3x- 4
ii) Another similar box is to be made such that its area of the base is given by the
polynomial P(y) having sum of the zeros as 7 and the product is 10. Then the
length and the breadth of the box are
A) (y+2).(y+5)
D) (y+2)(y-5)
B)(y-2).(y+5) C)y-2).(y-5)
iv) A third box has the area of the rectangular faces as r(s). If two zeroes of r(s)
are 3 and-5 then r(s) is
C)s+2s+15
D)s'+2s-15
B)s-2s-15
A)s-8s+15
v)The area of the top of the box is ra) = 5 a* - 7 a +k. If the zeroes of r(a) are
reciprocal of each other then k is​

Answer 1

Answer:

how I can read this much

Answer 2

Solution :-

Let width of the box = x unit .

so,

→ Length = (x + 3) unit

→ Height = (x - 2) unit

then,

→ Volume of box = L * B * H = x * (x + 3) * (x - 2) = x(x² - 2x + 3x - 6) = x(x² + x - 6) = (x³ + x² - 6x)

now,

→ Area of paper used to make the box = 2(LB + BH + HL) = 2[(x+3)x + x(x-2) + (x-2)(x+3)] = 2[x² + 3x + x² - 2x + x² + x - 6] = 2(3x² + 2x - 6) = (6x² + 4x - 12)

now, for another box sum of zeroes is 7 and product of zeroes 10 .

so,

→ y² - 7y + 10

→ y² - 5y - 2y + 10

→ y(y - 5) - 2(y - 5)

→ (y - 5)(y - 2)

now, for third box

→ sum of zeroes = 3 + (-5) = (-2)

→ product of zeroes = 3 * (-5) = (-15)

so,

→ Area of rectangular face = L * B = (s² + 2s - 15)

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