Question

true or falses the sum of zeros of x2+6x+7 is 6 ​

Answer 1

Answer:

No, the sum is -6.

Step-by-step explanation:

There's multiple ways to approach this problem.

One way is simply finding all the zeros of $x^2 + 6x+7$, which would give

$x_1 = -3+\sqrt{2}, \quad x_2=-3 -\sqrt{2}.$

(this can easily be done with the quadratic formula)

Adding the roots then gives $x_1 + x_2 = -6$

There's also this theorem that says that for all polynomials of the form

$x^2 + bx + c^2$, then the sum of the roots, let us call them $\beta$ and $\alpha$, is given by

$-b = \beta + \alpha$. Hence we see that the sum of roots must be -6.

Similarily, the product of the roots is given by $c = \alpha \beta$.