Example : Using the discriminate determine which solution set we get for
each of the following quadratic equations.
(a)
13x2 +1 = 5x
(b)
6q2 + 20q = 3
(c)
49t2 + 126t + 81 = 0
Solution
All we need to do here is make sure the equation is in
standard form, determine the value of a, b, and c, then
plug them into the discriminate.
(a) 13x2 +1 = 5x
First get the equation in standard form.
13x2 − 5x + 1 = 0
We then have,
a = 13 b = − 5 c
= 1
Plugging into the discriminate gives,
b2 − 4ac = (−5)2 − 4(13)(1) = −27
The discriminate is negative and so we will have two
complex solutions. For reference purposes
the actual solutions are,
(b)
6q2 + 20q = 3
Again, we first need to get the equation in standard
form.
6q2 + 20q − 3 = 0
This gives,
a = 6 b = 20 c
= −3
The discriminate is then,
b2 − 4ac = (6)2 − 4(20)(−3) = 276
The discriminate is positive we will get two real
distinct solutions. Here they are,
(c)
49t2 + 126t + 81 = 0
This equation is already in standard form so let’s jump
straight in.
a = 49 b = 126 c
= 81
The discriminate is then,
b2 − 4ac = (126)2 − 4(49)(81) = 0
In this case we’ll get a double root since the
discriminate is zero. Here it is,
.
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