11. Solve: (x - 2)(x ^ 2 - 9x + 13) + 5 = 0

Step-by-step explanation:

Start multiplying and adding all together. You get.

At this point we're stuck factoring since there exist a formula for the roots, but it's nowhere easy to remember. We start writing down The List (rational root theorem: it's the divisor of the constant term divided by the divisor of the lead coefficent, with a plus or minus, in our case it's ) and let's try checking one by one.

Value gives a zero on the LHS, it means the polynomial is divisible by . By doing the division, or writing it as , multiplying on the LHS and then finding the values of a, b, and c (easiest for me, your mileage may vary) we can write our expression, finally, as

At this point you can either apply the quadratic formula or decompose again the second factor as

by finding two numbers whose sum is -10 and product is 21, ie -3 and -7. At this point the expression

is true if

..

step-by-step explanation:

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.