Question

Знайдіть коефіцієнт q квадратного рівняння х2+рх+q=0, якщо його коренями є числа -2 і 3.

Answer 1

Ответ:

$(x - x _{1})(x - x_{2}) = 0$

$x_{1}=-2 \\ x_{2}=3$

$(x - ( - 2))(x - 3) = 0 \\ (x + 2)(x - 3) = 0 \\ {x}^{2} - 3x + 2x - 6 = 0 \\ {x}^{2} - x - 6 = 0$

q=-6

Answer 2

Дано рівняння х²+рх+q=0, корені рівняння х1 та х2 дорівнюють -2 та 3 відповідно.

За теоремою Вієта: х1+х2=-р; х1*х2=q щоб знайти q, ми замість х1 та х2 підставимо значення які нам дано, тобто -2*3=q, звідси випливає що q=-6

ВІДПОВІДЬ: q=-6

Answer 3

Finding the Coefficient q of a Quadratic Equation

To find the coefficient q of the quadratic equation x^2 + rx + q = 0, given that its roots are -2 and 3, we can use the fact that the sum and product of the roots of a quadratic equation are related to its coefficients.

The sum of the roots of the quadratic equation is equal to the negation of the coefficient of the linear term (r), divided by the coefficient of the quadratic term (1). In this case, the sum of the roots is -2 + 3 = 1.

The product of the roots of the quadratic equation is equal to the constant term (q), divided by the coefficient of the quadratic term (1). In this case, the product of the roots is (-2)(3) = -6.

Using these relationships, we can set up the following equations:

Sum of the roots: -r/1 = 1 Product of the roots: q/1 = -6

Simplifying these equations, we get:

-r = 1 q = -6

Therefore, the coefficient q of the quadratic equation x^2 + rx + q = 0, with roots -2 and 3, is q = -6.