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If (a) and (ß) are zeroes of the polynomial x^2-2x-8,then form a quadratic polynomial whose zeroes are 2/a and 2/ß. (a=alpha,ß=beta) |
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Answer» Answer: 2x² + x - 1 Step-by-step EXPLANATION: Polynomials in form of x^2 - Sx + P, represent S as sum of roots and P as PRODUCT of roots. Here, if a and ß are roots: • a + ß = 2 • aß = - 8 Let the required polynomial be x² - px + q, and 2/a & 2/ß are roots, so p = 2/a + 2/ß = 2(1/a + 1/ß) p = 2(a + ß)/aß = 2(2)/(-8) p = -1/2 Also, q = (2/a)(2/ß) q = 4(1/aß) q = 4{1/(-8)} = - 4/8 = -1/2 Therefore, polynomial is: x² - (-1/2)x + (-1/2) (2x² + x - 1)/2 Required polynomial is 2x² + x - 1 |
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