2. Find the sum of the zeroes of the polynomial 5x2 - 30x + 1.
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Answer:
The sum of zeroes of the polynomial ax
2
+bx+c=0 is
a
−b
.
Here the given equation is 5x
2
+3x+k=0.
Therefore, the sum of the zeroes is
5
−3
.
Let the zeroes be α and β.
⇒ α+β=
5
−3
and αβ=
5
k
.
⇒ α
2
+β
2
=(α+β)
2
−2αβ.
⇒
25
−11
=
25
9
−
5
2k
⇒
5
2k
=
25
20
⇒ k=2
Step-by-step explanation:
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