Question

Разложите квадратный трехчлен на множители x^2-x-1 РЕШИТЕ ПОЖАЛУЙСТА

Answer 1

Ответ:

Объяснение:

D=1-4*1*(-1)=5,  x1=1+V5 /2,  x2=1-V5 /2

ax^2+bx+c=a(x-x1)(x-x2)

x^2 -x -1= (x- (1+V5)/2) * (x- (1-V5) /2)  (V- корень)

Answer 2

Factoring the Quadratic Trinomial

To factor the quadratic trinomial x^2 - x - 1, we can use the quadratic factoring method. The goal is to find two binomials whose product is equal to the given trinomial.

Let's proceed with factoring the quadratic trinomial step by step:

Step 1: Identify the values of a, b, and c in the quadratic trinomial ax^2 + bx + c. In this case, a = 1, b = -1, and c = -1.

Step 2: Find two numbers, m and n, whose product is equal to ac (the product of a and c) and whose sum is equal to b. In this case, ac = 1 * -1 = -1 and b = -1. We need to find two numbers whose product is -1 and whose sum is -1.

Step 3: The numbers that satisfy the conditions in Step 2 are m = -1 and n = 1.

Step 4: Rewrite the quadratic trinomial using the values of m and n as follows:

x^2 - x - 1 = x^2 + mx + nx - 1

Step 5: Group the terms and factor by grouping:

x^2 + mx + nx - 1 = (x^2 + mx) + (nx - 1) = x(x + m) + (n(x - 1))

Step 6: Factor out the common factors from each group:

x(x + m) + (n(x - 1)) = x(x + m) - (x + m) = (x + m)(x - 1)

Step 7: Substitute the values of m and n:

(x + m)(x - 1) = (x - 1)(x + 1)

Therefore, the factored form of the quadratic trinomial x^2 - x - 1 is (x - 1)(x + 1).

Please let me know if you have any further questions!