find a quadratic polynomial which the given number as the sum and product of its zeroes respectively -1/4 -1/4 0,√5
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Answer:
P(x)=x
2
−(sum−of−roots)x+(product−of−roots)
(i)
x
2
−(
4
1
)x−1=0
⇒4x
2
−x−4=0
(ii)
x
2
−(
2
)x+
4
1
=0
⇒4x
2
−4
2
x+1=0
(iii)
x
2
−(0)x+
5
=0
⇒x
2
+
5
=0
(iv)
x
2
−(1)x+1=0
⇒x
2
−x+1=0
(v)
x
2
−(−
4
1
)x+
4
1
=0
4x
2
+x+1=0
(vi)
x
2
−(4)x+1=0
⇒x
2
−4x+1=0
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