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Byju's Answer
Standard X
Mathematics
Formation of a Quadratic Equation From It's Roots
Find the zero...
Question
Find the zeros of the quadratic polynomial
f
x
=
4
3
x
2
+
5
x
-
2
3
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Solution
To find the zeros of the quadratic polynomial we will equate f(x) to 0
∴
f
x
=
0
⇒
4
3
x
2
+
5
x
-
2
3
=
0
⇒
4
3
x
2
+
8
x
-
3
x
-
2
3
=
0
⇒
4
x
3
x
+
2
-
3
3
x
+
2
=
0
⇒
3
x
+
2
4
x
-
3
=
0
⇒
3
x
+
2
=
0
or
4
x
-
3
=
0
⇒
x
=
-
2
3
or
x
=
3
4
Hence, the zeros of the quadratic polynomial
f
x
=
4
3
x
2
+
5
x
-
2
3
are
-
2
3
or
3
4
.
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Q.
If α and β are the zeros of the quadratic polynomial f(x) = x
2
− 5x + 4, find the value of
1
α
+
1
β
-
2
αβ
.