Question

if x ^ 2 - 12x - 64 = 0 and q and p are Solutions then.....A. q = 15 and p = -3B. q + p = - 12 and pq = 64C. q + p = - 12 and pq = - 64D. q + p = - 64 and pq = - 12E. Other and why

Answer 1

The general for of a quadratic equation is:

ax² + bx + c = 0

You have the following quadratic equation:

x² - 12x - 64 = 0

In order to solve the previous equation you use the quadratic formula, given by:

x = (-b ± √(b² - 4ac)) /2a

In this case, for the given equation you have a=1, b=-12 and c=-64. You replace the values of all paramters in the quadratic formula:

x = (-(-12) ± √((-12)² - 4(1)(-64)) )/2(1)

x = (12 ± √(144 + 256))/2

x = (12 ± √(400))/2

x = (12 ± 20)/2

Hence, the two solutions x1 and x2 are:

x1 = (12 + 20)/2 = 32/2 = 16

x2 = (12 - 20)/2 = -8/2 = -4

But x1 and x2 are the solution p and q. In this case any of the given options accomplishes with the obtained values of x1 and x2. Hence the answer is:

E. Other and why