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if alpha and beta are the zeros of the quadratic polynomial f(x) = x^2 - 1 , find a quadratic polynomial whose zeroes are 2α/β and 2β/α |
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Answer» Step-by-step explanation: F(x)=x²-1 Roots are ALPHA ,beta Alpha +Beta=-b/a=0 Alpha×beta=c/a=-1 Now we have to Find Polynomial whose ROOT are 2alpha/beta,2beta/alpha Now we Structure of Quadratic Equation ax²+(SUM of Roots)x+product of Roots So sum of Roots 2alpha/beta+2beta/alpha 2alpha²+2beta²/alpha×beta (For Convience i m taking alpha=x,beta=y) 2x²+2y²/xy 2(x²+y²)/xy We know (x+y)²-2xy=x²+y² 0²-2×-1=x²+y² x²+y²=2 xy=-1 Sum of Roots 4/-1=-4 Product of Roots 4xy/xy =4 Sum=-4 product=4 Quadratic Equation x²+4x+4 p(x)=x²+4x+4 |
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