Question

5)В уравнении x^2+px-16=0 один из корней равен 8. Найди второй корень и коэффициент р помогите пожалуйста!!!

Answer 1

X^2+px-16=0 решаем используя теорему Виета: х1+х2=-р. х1·х2=-16. по условию х1=8, тогда 8·х2=-16. х2=-2.
8+(-2)=6.
р=6.
ответ: р=6; х2=-2.

Answer 2

Finding the Second Root and Coefficient p in the Equation x^2 + px - 16 = 0

To find the second root and coefficient p in the equation x^2 + px - 16 = 0, we can use the fact that one of the roots is given as 8. Let's proceed with the solution:

1. We know that the sum of the roots of a quadratic equation is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term. In this case, the sum of the roots is -p.

2. Since one of the roots is given as 8, the sum of the roots is 8 + second root = -p.

3. Therefore, the second root can be found by subtracting 8 from the sum of the roots: second root = -p - 8.

4. Now, let's find the coefficient p. We can use the fact that the product of the roots of a quadratic equation is equal to the constant term divided by the coefficient of the quadratic term. In this case, the product of the roots is -16.

5. Since one of the roots is 8, the product of the roots is 8 * second root = -16.

6. Therefore, we can solve for the second root: second root = -16 / 8 = -2.

7. Now, substituting the value of the second root (-2) into the equation second root = -p - 8, we can solve for the coefficient p:

-2 = -p - 8 -p = -2 + 8 -p = 6 p = -6.

Therefore, the second root of the equation x^2 + px - 16 = 0 is -2, and the coefficient p is -6.

Answer: The second root of the equation x^2 + px - 16 = 0 is -2, and the coefficient p is -6.