Question

В уравнении x²+11x+q=0 один из корней равен -7. Найдите другой корень и коэффициент q. Помогите пожалуйста оочень надо(

Answer 1

По теореме Виета:

х1*х2=q

х1+х2=-11

 

у нас по условию один корень равен -7.Подставляем:

х1+(-7)=-11

отсюда

 х1=-11+7=-4

 

-4*-7=28

q=28 

Answer 2

Solving for the Other Root and Coefficient q

To find the other root and the coefficient q in the equation x² + 11x + q = 0, given that one of the roots is -7, we can use the fact that the sum of the roots in a quadratic equation is equal to the negation of the coefficient of x divided by the coefficient of x².

Let's denote the roots as r and s. Then, we have the following relationships: 1. r + s = -11 2. r * s = q

Given that one of the roots is -7, we can use the sum of roots relationship to find the other root and then calculate the coefficient q.

Using the sum of roots relationship: -7 + s = -11 s = -11 + 7 s = -4

Now, we can calculate the coefficient q using the product of roots relationship: q = -7 * -4 q = 28

Therefore, the other root is -4 and the coefficient q is 28.