Question

R) p2 + 100p + 200 = 0

Answer 1

Пошаговое объяснение:

D=100^2-4×200=10000-800=9200

√9200=20√23

x1=(-100-20√23)/2

x2=(-100+20√23)/2

Answer 2

To solve the quadratic equation p^2 + 100p + 200 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the given equation p^2 + 100p + 200 = 0, we can identify that a = 1, b = 100, and c = 200. Plugging these values into the quadratic formula, we get:

p = (-100 ± √(100^2 - 4 * 1 * 200)) / (2 * 1)

Simplifying further:

p = (-100 ± √(10000 - 800)) / 2

p = (-100 ± √(9200)) / 2

Now, we can calculate the two possible solutions for p:

p = (-100 + √9200) / 2 p = (-100 + 95.87) / 2 p = -4.13 / 2 p ≈ -2.07

and

p = (-100 - √9200) / 2 p = (-100 - 95.87) / 2 p = -195.87 / 2 p ≈ -97.94

Therefore, the solutions to the equation p^2 + 100p + 200 = 0 are approximately p ≈ -2.07 and p ≈ -97.94.