If the quadratic equation
1
3x x 3
x
+ = + is written in standard form, then
a) a = 3, b = 3, c = 1 b) a = 3, b = – 3, c = 1
c) a = 2, b = – 3, c = 1 d) a = 3, b = – 3, c = 3
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Answer:
The standard form of a quadratic equation is ax
2
+bx+c=0,a
=0.
(That is, when the terms of the quadratic equation are written in descending order of their degrees, then we get the standard form of the equation.)
For the equation 3x
2
+5
2
x+2=0, we get
a=3,b=5
2
,c=2
Using the general form, we get
D=b
2
−4ac(5
2
)
2
−4(3)(2)=26.
Here, D > 0, so the equation has real and distinct roots.
Let the roots be α and β.
So, α=
2a
−a+
D
and β=
2a
−b−
D
⇒α=
2(3)
−5
2
+
26
and β=
2(3)
−5
2
−
26
⇒α=
6
−5
2
+
26
and β=
6
−5
2
−
26
∴ Roots of the given equation are
6
−5
2
+
26
and
6
−5
2
−
26
.
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