What values of x cannot be used if the above six fields are to be built together?

Question

1. Strawberry field with area 16x2+4x
2. Cucumber field with area x2-4x-21
3. Tomato field with area x2-36
4. Parsley field with area x2-10x+21
5. Onion field with area x2-11x+30
6. Watermelon field with area x2+8x-20

What values of x cannot be used if the above six fields are to be built together?

Answer 1

Any value of x that produces a field area that is NOT positive can not be used (that is, x must produce area>0).

S: 16x² + 4x = 4x(4x+1) is not positive for 0.25 ≤ x ≤ 0

C: x² - 4x - 21 = (x+3)(x-7) is not positive for -3 ≤ x ≤ 7

T: x² - 36 = (x+6)(x-6) is not positive for -6 ≤ x ≤ 6

P: x² - 10x + 21 = (x-3)(x-7) is not positive for -3 ≤ x ≤ 7

O: x² - 11X + 30 = (x-5)(x-6) is not positive for 5 ≤ x ≤ 6

W: x² + 8x - 20 = (x+10)(x-2) is not positive for -10 ≤ x ≤ 2

Combining these ranges (to get the maximum), we get -10 ≤ x ≤ 7

Values between -10 and 7 (inclusive) may not be used because they produce a field area of non-positive.

Answer 2

The sum of the areas is 21x² - 13x - 8

The solutions are -8/21 and 1

So any value of x other than these two do not be used.