find the zeroes of the polynomial y2-5y+6=0 also verify the relationship between their zeroes
Answers
Step-by-step explanation:
The quadratic polynomial is y
2
+
2
3
5
y−5.
The zeros of the polynomial are:
y
2
+
2
3
5
y−5=0
⟹ y
2
+2
5
y−
2
5
y−5=0
⟹ y(y+2
5
)−
2
5
(y+2
5
)=0
⟹ (y+2
5
)(y−
2
5
)=0
⟹ y−2
5
and y=
2
5
=0
The zeros are −2
5
and
2
5
.
Now verifying the relation of zeros with the coefficients of the quadratic polynomial y
2
+
2
3
5
y−5:
Comparing it with the standard from of quadratic equation ax
2
+bx+c, we get, a=1, b=
2
3
5
and c=−5
Thus,
Sum of the zeros =−2
5
+
2
5
=
2
−4
5
+
5
=
2
−3
5
=−
a
b
.
Product of the zeros =−2
5
×
2
5
=−5
=
a
c
.
Hence, verified.
Therefore, option A is correct.
Answer:
Step-by-step explanation:
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