Question

An open box is to be made from a rectangular piece of cardboard that measures 6 in. by 3 in., by cutting out squares of the same size from each corner and bending up the sides. Is it possible to cut the squares so that the volume of the box is 40 in.3? volume of the box Find all real solutions of this equation to answer the question. (6 – 2x)(3 – 2x)x = 40 Yes. Because mc001-1.jpg is a root, you can cut squares with sides of mc001-2.jpg in. to make the box No. This equation has no real solutions. No. The only real solution is x = 4. It is not possible to cut squares of this size.

Answer 1

No. The only real solution is x = 4. It is not possible to cut squares of this size.

Answer 2

Answer:

No. The only real solution is x = 4. It is not possible to cut squares of this size.

Step-by-step explanation:

Volume of the box is (6 - 2x)(3 - 2x)x = 40

2(3 - x)(3 - 2x)x = 40

Divide both sides by 2.

(3 - x)(3 - 2x)x = 20

$(9-6x-3x+2x^{2})x =20$

$(9 - 9x+2x^{2} )x=20$

$2x^{3} -9x^{2} +9x-20=0$

On inspection, x = 4 is one of the solutions of the above cubic equation.

Now, divide the equation by x - 4, we get

$2x^{2} -x+5=0$

The discriminant of this equation is:

$(-1)^{2}-4(2)(5)=1-40$

= -39 < 0

Hence, x = 4 is the only real solution.

Since, 6 - 2x < 0, it is not possible to cur squares of side 4 in. at the corners.

Hence, the correct answer is:

No. The only real solution is x = 4. It is not possible to cut squares of this size.