SOLUTION: a) For the quadratic equation kx^2 + 2x + 4 = 0, find the value of k so that the roots are equal (there is only one root). b) The roots of x^2 + (k + 8)x + 9k = 0 are equal. What

Algebra ->  Test  -> Lessons -> SOLUTION: a) For the quadratic equation kx^2 + 2x + 4 = 0, find the value of k so that the roots are equal (there is only one root). b) The roots of x^2 + (k + 8)x + 9k = 0 are equal. What      Log On


   

Question 211094: a) For the quadratic equation kx^2 + 2x + 4 = 0, find the value of k so that
the roots are equal (there is only one root).
b) The roots of x^2 + (k + 8)x + 9k = 0 are equal. What are the value(s) of
k?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
For the quadratic equation kx^2 + 2x + 4 = 0, find the value of k so that
the roots are equal (there is only one root).
:
Use the discriminant: a=k; b=2; c=4
b^2 - 4ac = 0 means equal roots
2^2 - 4*k*4 = 0
4 - 16k = 0
-16k = -4
k = %28-4%29%2F%28-16%29
k = +.25 (=a)
:
.25x^2 + 2x + 4 = 0
:
get rid of the decimal, multiply by 4
x^2 + 8x + 16 = 0
Factors to
(x+4)(x+4) = 0
x = -4 is the single root
:
:
b) The roots of x^2 + (k + 8)x + 9k = 0 are equal. What are the value(s) of
k?
Use the discriminant: a=1; b=(k+8); c=9k
b^2 - 4ac = 0 means equal roots
(k+8)^2 - 4*1*(9k) = 0
k^2 + 16k + 64 - 36k = 0
k^2 - 20k + 64 = 0
(k-16)(k-4) = 0
k = 16
and
k = 4
:
When k=16 then b=24, and c=144 (9*16)
x^2 + 24x + 144
Factors
(x+12)(x+12) = 0
x = -12 is the single root
:
When k=4, then b=12, and c=36
x^2 + 12x + 36
Factors
(x+6)(x+6) = 0
x = -6 is the single root