1. If α and β are zeroes of the quadratic polynomial 4x2+4x+1 , form a quadratic polynomial whose zeroes are 2α and 2β.
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Answered by
10
4x^2 + 4x +1
4x^2 +2x+2x+1
2x(2x+1)+1(2x+1)
(2x+1)(2x+1)
x=-1/2,x=-1/2.
Alpha = -1/2 and Beta =-1/2.
2alpha=2(-1/2)=-1.
2beta=2(-1/2)=-1
Sum of zeroes=-1+(-1)=-2.
Product of zeroes=-1 x -1 =1.
k[x^2-(Sum of zeroes)x+Product of zeroes]
k{x^2-(-2)x+1]
k[x^2+2x+1]
Hence,the required polynomial is x^2+2x+1.
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4x^2 +2x+2x+1
2x(2x+1)+1(2x+1)
(2x+1)(2x+1)
x=-1/2,x=-1/2.
Alpha = -1/2 and Beta =-1/2.
2alpha=2(-1/2)=-1.
2beta=2(-1/2)=-1
Sum of zeroes=-1+(-1)=-2.
Product of zeroes=-1 x -1 =1.
k[x^2-(Sum of zeroes)x+Product of zeroes]
k{x^2-(-2)x+1]
k[x^2+2x+1]
Hence,the required polynomial is x^2+2x+1.
Hope it helps u...
please mark it as brainliest..
Answered by
3
Answer:
Step-by-step explanation:
4x^2 + 4x +1
4x^2 +2x+2x+1
2x(2x+1)+1(2x+1)
(2x+1)(2x+1)
x=-1/2,x=-1/2.
Alpha = -1/2 and Beta =-1/2.
2alpha=2(-1/2)=-1.
2beta=2(-1/2)=-1
Sum of zeroes=-1+(-1)=-2.
Product of zeroes=-1 x -1 =1.
k[x^2-(Sum of zeroes)x+Product of zeroes]
k{x^2-(-2)x+1]
k[x^2+2x+1]
Hence,the required polynomial is x^2+2x+1.
Hope it helps UU...
please mark it as brainliest..
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