If α and β are the zeroes of polynomial x2 + x – 2, find a polynomial whose zeroes are 2α+1 and 2β+1
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Answer:
Since α,β are the zeroes of the polynomial f(x)=x
2
−2x−3
α+β=−
a
b
=−(−2)=2
αβ=
a
c
=−3
sum of the zeroes of the required polynomial
=(2α−1)+(2β−1)=2(α+β)−2
=2×2−2=2
product of the zeroes =(2α−1)(2β−1)
4αβ−2α−2β+1
=4×−3−2(α+β)+1
=−12−2×2+1=−15
sum of zeroes =2=−
a
b
product of zeroes =−15=
a
c
If a=1, then b=−2,c=−15 in ax
2
+bx+c
The required polynomial is x
2
−2x−15
Step-by-step explanation:
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