Question

X^2 + px - 35 = 0 x1=7 x2-? p-?

Answer 1

Используем теорему Виета
х₁*х₂ = - 35
7х₂ = - 35
х₂ = -5

х₁ + х₂ = - р
7 + (-5) = -р
-р = 2
р = -2

Answer 2

To find the values of x2 and p for the quadratic equation x^2 + px - 35 = 0, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 1, b = p, and c = -35. We already have one root, x1 = 7. Now, let's find x2 and p.

First, plug in the values:

1. For x1 = 7: x1 = (-p + √(p^2 - 4(1)(-35))) / (2(1)) 7 = (-p + √(p^2 + 140)) / 2

Now, solve for p:

7 * 2 = -p + √(p^2 + 140) 14 = -p + √(p^2 + 140)

Move -p to the other side:

√(p^2 + 140) = 14 + p

Square both sides to eliminate the square root:

p^2 + 140 = (14 + p)^2 p^2 + 140 = 196 + 28p + p^2

Now, subtract p^2 from both sides to simplify:

140 = 196 + 28p

Subtract 196 from both sides:

-56 = 28p

Now, divide by 28 to find p:

p = -56 / 28 p = -2

So, the value of p is -2.

Now that we have found p, we can use it to find x2:

x2 = (-p - √(p^2 - 4ac)) / (2a) x2 = (-(-2) - √((-2)^2 - 4(1)(-35))) / (2(1)) x2 = (2 - √(4 + 140)) / 2 x2 = (2 - √144) / 2 x2 = (2 - 12) / 2 x2 = -10 / 2 x2 = -5

So, the value of x2 is -5, and the value of p is -2 for the given quadratic equation.