Question

один із коренів квадратного рівняння х2-5х+q=0 дорівнює -3 знайди коефіцієнт q та другий корінь рівняння

Answer 1

Другий корінь 8

Коефіцієнт q = -24

розв’язання на фото

Answer 2

Finding the Coefficient q and the Second Root of the Equation

To find the coefficient q and the second root of the 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 is equal to the negation of the coefficient of the linear term (x) divided by the coefficient of the quadratic term (1). Additionally, the product of the roots is equal to the constant term (q) divided by the coefficient of the quadratic term (1).

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

First, let's find the coefficient q: We know that the product of the roots is equal to q/1, and one of the roots is -3. Therefore, the product of the roots is -3 times the second root. This means that q is equal to the product of the roots, which is -3 times the second root.

Now, let's find the second root: We know that the sum of the roots is equal to -(-5)/1, which simplifies to 5. Since one root is -3, the other root must be 5 - (-3), which equals 8.

Therefore, the coefficient q is -3 times the second root, and the second root of the equation is 8.

Coefficient q: -3 times the second root Second root: 8

Conclusion

The coefficient q is -3 times the second root, and the second root of the equation is 8.