Find k, so that x^2 + kx + 144 = 0 has equal roots. How would i solve this?

Answer 1

for equal roots b^2=4ac
k^2=576
k=+/-24
so the equation is x^2+24x+144=0 or x^2-24x+144=0

Answer 2

If x^2 + kx + 144 has equal roots, say these roots are a and a.
Then (x-a)*(x-a) = 0, or x^2-2ax+a^2 = 0.
So a^2 == 144, so a = 12 or a = -12.
So k = -2a, so k = -24 or 24 accordingly.

Answer 3

For equal roots, the factorization has to be (x+a)^2, therefore a^2 = 144 and a = -12 or +12. Put that back in the original equation, and it follows that k = +24 or -24.

Answer 4

You must find x first before being able to find k.

x^2 + kx + 144 = 0
(x + 12)(x + 12) = 0
(x - 12)(x - 12) = 0

If x = 12, then k = -24
If x = -12, then k = 24

Answer 5

Factor the equation. You want two identical numbers that will multiply to be 144. 12 times 12 = 144 so k=12. You could also see this if you used a graphing calculator. The graph crosses the x axis at 12

Answer 6

[-k +- sqrt(k^2 - 4*1*144) ]/ 2

k can be anyting as long as k^2 > 4*144
k^2 > 576

k < -24 or k > 24

at k = 24, there is one root.

Answer 7

ax^2+bx+c=0

Insert into Quadratic Equation
x= -b +- square root of b^2 - 4ac / 2a

Answer 8

Just plug in to equation. It will give you the roots in terms of k.

http://en.wikipedia.org/wiki/Quadratic_equation
http://mathworld.wolfram.com/QuadraticEquation.html

Answer 9

It's a quadratic equation. It can't be fully solved without a value for "k"