Ifαand β , are the zeros of the polynomials f(x) = x2 – 2x + 5, then find the quadratic polynomial whose zeroes are α + β and 1/alpha+1/beta
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in x²-2x+5
α+β=-2 and αβ=5 and hence if α+β is a root then -2 is one root and if 1/α+1/β is a root then by taking LCM α+β/αβ is a root ,which we already know as -2/5 . hence the polynomial is {x-(α+β)}{x-(1/α+1/β)} ,which is {x-(-2)}{x-(-2/5)} ={x+2] [x+2/5]=5x²+12x +4
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in x²-2x+5
α+β=-2 and αβ=5 and hence if α+β is a root then -2 is one root and if 1/α+1/β is a root then by taking LCM α+β/αβ is a root ,which we already know as -2/5 . hence the polynomial is {x-(α+β)}{x-(1/α+1/β)} ,which is {x-(-2)}{x-(-2/5)} ={x+2] [x+2/5]=5x²+12x +4
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