Question

складіть рівняння, яке : 1) має єдиний корінь, що дорівнює числу -4 ; 2) має безліч коренів; 3) не має коренів. (срочно , помогите пожалуйста )​

Answer 1

Ответ:

$1)\ \ x=-4:\ \ \ \ \ x^2+8x+16=0\\\\2)\ \ x\in R:\ \ \ x=x\\\\3)\ \ x\in \varnothing :\ \ \ \dfrac{1}{x^2+1}=0$

Answer 2

Equation with a Single Root (-4):

To create an equation with a single root that equals -4, we can use the fact that if a quadratic equation has a single root, it means that the quadratic expression can be factored into a perfect square.

Let's assume the equation is in the form of ax^2 + bx + c = 0. Since the root is -4, we can write the equation as (x + 4)^2 = 0. Expanding this equation, we get x^2 + 8x + 16 = 0.

Therefore, the equation with a single root of -4 is x^2 + 8x + 16 = 0. [[1]]

Equation with Infinite Roots:

To create an equation with infinite roots, we need an equation that is always true, regardless of the value of x. One such equation is 0 = 0. This equation is true for all values of x, which means it has infinite roots.

Therefore, the equation with infinite roots is 0 = 0.

Equation with No Roots:

To create an equation with no roots, we need an equation that is never true for any value of x. One such equation is 1 = 0. Since 1 is never equal to 0, this equation has no roots.

Therefore, the equation with no roots is 1 = 0.

I hope this helps! Let me know if you have any further questions.