Find a quadratic polynomial whose zeroes are 3 - √5, 3 + √5.
class 10th
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1
Answer:
Let α=3+
5
and β=3
5
Sum of zeros =α+β=3+
5
+3−
5
=6
Product of zeros =αβ=(3+
5
)(3−
5
)=9−5=4
Also, Sum of roots =
a
−b
=−
1
6
Product of roots =
a
c
=
1
4
⟹a=1,b=−6 and c=4
Hence, the quadratic polynomial is x
2
−6x+4
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