Find a quadratic polynomial whose zeroes are reciprocals of the polynomial p(x)=x2-x-2
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p(x)=x²-x-2
Finding the zeros of p(x) by setting p(x) = 0
x²-x-2 = 0
x² + x - 2x - 2 = 0
x(x+1) -2(x+1)
(x-2)(x+1) = 0
x = -1 or x = 2
Reciprocals are: -1 and 1/2
Equation:
x=-1 or x = 1/2
x+1 = 0 and x-1/2 = 0
(x+1)(x-1/2) = 0
x² + x/2 - 1/2 = 0
2x² + x - 1 = 0
Finding the zeros of p(x) by setting p(x) = 0
x²-x-2 = 0
x² + x - 2x - 2 = 0
x(x+1) -2(x+1)
(x-2)(x+1) = 0
x = -1 or x = 2
Reciprocals are: -1 and 1/2
Equation:
x=-1 or x = 1/2
x+1 = 0 and x-1/2 = 0
(x+1)(x-1/2) = 0
x² + x/2 - 1/2 = 0
2x² + x - 1 = 0
Answered by
1
Answer:
Step-by-step explanation:
p(x)=x²-x-2
Finding the zeros of p(x) by setting p(x) = 0
x²-x-2 = 0
x² + x - 2x - 2 = 0
x(x+1) -2(x+1)
(x-2)(x+1) = 0
x = -1 or x = 2
Reciprocals are: -1 and 1/2
Equation:
x=-1 or x = 1/2
x+1 = 0 and x-1/2 = 0
(x+1)(x-1/2) = 0
x² + x/2 - 1/2 = 0
2x² + x - 1 = 0
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