The correct Option is (A) 35x^3 - 16x^2 + 44x - 48

Explanation: The product of the polynomials (5x^2 + 2x +8)(7x-6) is:

(5x^2)(7x-6) + 2x(7x-6) +8(7x-6)

35x^3 -30x^2 + 14x^2 - 12x + 56x - 48
35x^3 - 16x^2 + 44x - 48 (Option A)

6 0

3 years ago

The roots of the quadratic equation $z^2 + bz + c = 0$ are $-7 + 2i$ and $-7 - 2i$. What is $b+c$?

Alexxx [7]

Answer:

Step-by-step explanation: Given the quadratic equation $z^2 + bz + c = 0$, Vieta's formulas tell us the sum of the roots is $-b$, and the product of the roots is $c$. Thus,

\[-b = (-7 + 2i) + (-7 - 2i) = -14,\]so $b = 14.$

Also,

\[c = (-7 + 2i)(-7 - 2i) = (-7)^2 - (2i)^2 = 49 + 4 = 53.\]Therefore, we have $b+c = \boxed{67}$.

There are many other solutions to this problem. You might have started with the factored form $(z - (-7 + 2i))(z - (-7 - 2i)),$ or even thought about the quadratic formula.

This is the aops answer :)

8 0

2 years ago