Step by step
The question
Question: for which k does 4x² + kx + 1 = 0 have exactly one solution?
1 Find a, b and c
We read the numbers.
a = 4 is with x².
With x is the letter k.
c = 1 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 4 times 1 is 16.
Now we have k² − 16 = 0.
4 Remove the − 16
We want k² alone.
− 16 is in the way.
So we add 16 on both sides.
We add 16 on both sides.
They stay equal.
− 16 and + 16 make zero.
Cross them out.
Now we have k² = 16.
5 Find k
Which numbers times themselves make 16?
4 times 4 is 16.
And −4 times −4 is 16 too: minus times minus is plus.
Careful!
k = −4 works too.
(−4)² is 16.
So k = 4 or k = −4.
6 Check
Let's check.
k = 4: 4 squared is 16, and 16 − 16 is 0.
And k = −4: (−4) squared is 16, and 16 − 16 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 − 16.
Then: find k.
Last: check.