A 64-inch board is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is 5 times as long as the first piece. Find the length of the longest piece.

Explanation:

x is some positive real number, and the units of each are in inches.

Add up the smaller pieces and we should get 64 inches back again

x+2x+5x = 64

8x = 64

x = 64/8

x = 8

The first piece is 8 inches long.

2x = 2*8 = 16 is the length of the second piece (in inches)

The third piece is 40 inches because 5x = 5*8 = 40

Summary:

first = 8 inches

second = 16 inches

third = 40 inches

Check: 8+16+40 = 64, which confirms the answer

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

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