Question

Чи можна розкласти квадaртний трилен на множники ? 6х2 – 3х +5​

Answer 1

Ответ:

$6x^2-3x+5=0\ \ ,\ \ \ D=9-4\cdot 6\cdot 5=-111$

Так как D<0 , то уравнение не имеет действительных корней. Значит нет точек пересечения графика квадратичной функции с осью ОХ, то есть нет корней записанного уравнения. А поэтому нельзя разложить этот квадратный трёхчлен на множители .

Answer 2

Factoring a Quadratic Trinomial

Yes, it is possible to factor a quadratic trinomial. Let's factor the quadratic trinomial 6x^2 - 3x - 5.

To factor a quadratic trinomial of the form ax^2 + bx + c, we look for two numbers that multiply to ac (the product of the coefficient of x^2 and the constant term) and add to b (the coefficient of x). This process is known as "factoring by grouping."

Factoring the Quadratic Trinomial

To factor the given quadratic trinomial 6x^2 - 3x - 5, we need to find two numbers that multiply to (6 * -5) = -30 and add to -3. These numbers are -5 and 6.

Factored Form

The factored form of the quadratic trinomial 6x^2 - 3x - 5 is: 6x^2 - 3x - 5 = (2x - 5)(3x + 1)

This is the result of factoring the given quadratic trinomial using the method of factoring by grouping.

I hope this helps! If you have any further questions, feel free to ask.