In this equation, k is a constant…

Some help please, Mike?

x^2 – 12x +k = 0 In this equation, k is a constant. For which values of k does the equation have only one solution? I know I can set the discriminant to zero and solve for k. But is there another way to solve? Thanks!

sqrt(3m^2 + 24) = 2m + 2. What is the sum of all the solutions to the equation? I know how to find the sum algebraically, but why can’t I use the -b/a formula here? Is it because there’s a radical? Thank you!

Whenever you have to square both sides to solve, you have to check for extraneous solutions. That tells you m could be 2 or –10, but because part of the solution was squaring both sides, you need to run both possible solutions through the original equation.Try 2 first: That works, now how about –10? Nope. Remember (more…)

Test 7 Section 4 Question 6

Hi Mike…SAT 7, Section 4, Q6: I now see the shortcut here (that both sides of the equation are perfect squares,) but if I did expand and FOIL the left side, wouldn’t I still get the correct “a” values even though it takes longer? I can’t get it to work !! Can you please show the alternate path math steps? Or is recognizing the perfect squares the ONLY way to solve this one ? Thanks!

PWN the SAT Math Guide p. 120 #9

PWN the SAT Math Guide p. 122 (p. 120 in newer printing) #9

h = -4.9^2 + t + 1.5
The equation … After how many seconds will the coin land on the ground?

When the coin lands, y=0, so we just need to solve the quadratic. Using the quadratic formula, however, I get a messy repeating decimal, not .664, .665. Could you solve this for me using the quadratic formula?

Also, I tried to search the Q&A here to see if you had already answered this question. Could you make an index for PWN the SAT Math Gu