Step by step
The question
Question: for which k does x² + kx + 16 = 0 have exactly one solution?
1 Find a, b and c
We read the numbers.
a = 1 is with x².
With x is the letter k.
c = 16 is the plain number.
2 Choose the rule
From the discriminant lesson: the sign of b² − 4ac tells how many solutions there are.
We want exactly one solution.
So b² − 4ac must be 0.
We write it: b² − 4ac = 0.
3 Put the numbers in
We put in the numbers.
The letter k stays as it is: it is the number we want.
4 times 1 times 16 is 64.
Now we have k² − 64 = 0.
4 Remove the − 64
We want k² alone.
− 64 is in the way.
So we add 64 on both sides.
We add 64 on both sides.
They stay equal.
− 64 and + 64 make zero.
Cross them out.
Now we have k² = 64.
5 Find k
Which numbers times themselves make 64?
8 times 8 is 64.
And −8 times −8 is 64 too: minus times minus is plus.
Careful!
k = −8 works too.
(−8)² is 64.
So k = 8 or k = −8.
6 Check
Let's check.
k = 8: 8 squared is 64, and 64 − 64 is 0.
And k = −8: (−8) squared is 64, and 64 − 64 is 0.
Both give exactly one solution.
It works!
Let's look back.
First: find a, b and c.
Then: choose the rule.
Then: put the numbers in.
Then: remove the − 64.
Then: find k.
Last: check.