Question

Один з коренів рівняння х2+5х+q=0 дорівнює 3 знайти q та другій корінь

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

Solving the Quadratic Equation for q and the Second Root

To solve the given quadratic equation x^2 + 5x + q = 0 when one of the roots is 3, we can use the fact that the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is equal to -b/a and the product of the roots is equal to c/a.

Given that one of the roots is 3, we can use this information to find the value of q and the second root.

Let's proceed with the calculation.

Calculating q and the Second Root

Using the sum and product of the roots, we can calculate the value of q and the second root.

The sum of the roots is equal to -b/a, and the product of the roots is equal to c/a.

For the given equation x^2 + 5x + q = 0: - Sum of the roots = -5 - Product of the roots = q

Given that one of the roots is 3, we can use the sum of the roots to find the second root: - Sum of the roots = First root + Second root - -5 = 3 + Second root - Second root = -5 - 3 - Second root = -8

Now, we can use the product of the roots to find the value of q: - Product of the roots = 3 * (-8) = -24

Therefore, the value of q is -24, and the second root is -8.

So, for the equation x^2 + 5x + q = 0 when one of the roots is 3, the value of q is -24 and the second root is -8.

Conclusion

We have successfully calculated the value of q and the second root for the given quadratic equation based on the information provided.