sum and product of a roots

Mang Juan owns a rectangular lot. the perimeter of the lot is 90 m and its area is 450 m².

What equation represents the Perimeter and the Area of the lot?

PERIMETER = 2L + 2W

AREA= L * W

SOLUTIONS:

90 = 2L +2W 450 = L* W

45 = L + W 450 = L * W

Mang Juan owns a rectangular lot. the perimeter of the lot is 90 m and its area is 450 m².

Using the idea of the sum and product of roots of quadratic equation, how would you determine the length and the width of the rectangular lot?

What are the dimensions of the rectangular lot?

Let one number be x. Then the other number is 50/x.

x + 50/x = 27

X x => x2 + 50 = 27x

- 27x => x2 - 27x + 50 = 0

(x -25)(x -2) = 0

(x -25) = 0 or (x -2) = 0

x = 25 or x = 2.

h = -16t2  + 64t + 80

h = -16* 1*1 + 64*1 + 80 = 128m

What is the maximum height reached by the ball?

Rearrange by the completing the square, we get:

h = -16[t² - 4t - 5]

h = -16[(t - 2)² - 9]

h = -16(t - 2)² + 144

When the height is maximum, t = 2; therefore, maximum height = 144m.

When the ball hits the ground, h = 0;

-16t² + 64t + 80 = 0

Divide the equation by -16

 t² - 4t - 5 = 0

(t - 5)(t + 1) = 0

t = 5 or t = -1

The time cannot be negative; so, the time = 5 seconds.