x^2-13x+42=(x+a)(x+b)

Предыдущий
вопрос Следующий
вопрос

To find the values of a and b, we can expand the right side of the equation and compare it to the given equation.

(x+a)(x+b) = x^2 + (a+b)x + ab

Now, we know that the equation x^2 - 13x + 42 is equivalent to the expanded form x^2 + (a+b)x + ab. By comparing the coefficients of x and the constant term on both sides, we can determine the values of a and b.

From the equation x^2 - 13x + 42 = x^2 + (a+b)x + ab, we can see that:
a + b = -13
ab = 42

Now, we need to find two numbers that multiply to 42 and add up to -13. These two numbers are -6 and -7.

Therefore, a = -6 and b = -7.

So, x^2 - 13x + 42 = (x-6)(x-7).