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5. Find the quadratic polynomial whose zeroes are square of the zeroes of the polynomialx2-x-1 |
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Answer» First find roots of x^2-x-1hencex=-b+-√b^2-4ac/2ax=1+-√1+4/2x=1+√5/2 ,1-√5/2hence square will be y=(1+√5/2)^2,y=(1-√5/2)^2y=1+5+2√5/4,y=1+5-2√5/4y=6+2√5/4,y=6-2√5/4hencethe quadratic equation y^2-(sum of roots)y+(product of roots)hencey^2-(12/4)y+(36-10/16)y^2-3y+13/8 |
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