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| 1. |
6q square -7y+2 find the quadratic polynomial whose zeroes are 1by alfa and 1by beta |
| Answer» {tex}\\alpha \\ and\\ \\beta{/tex}\xa0are the roots of the polynomial, p(y) = 6y2 - 7y + 2a=6, b= -7, c= 2{tex} \\alpha + \\beta =-\\frac{b}{a}= - \\left( - \\frac { 7 } { 6 } \\right) = \\frac { 7 } { 6 }{/tex}and\xa0{tex}\\alpha \\beta = \\frac{c}{a} = \\frac { 2 } { 6 } = \\frac { 1 } { 3 }{/tex}Now,\xa0{tex}\\frac { 1 } { \\alpha } + \\frac { 1 } { \\beta } = \\frac { \\alpha + \\beta } { \\alpha \\beta } = \\frac { 7 / 6 } { 2 / 6 } = \\frac { 7 } { 2 }{/tex}and\xa0{tex}\\frac { 1 } { \\alpha } \\times \\frac { 1 } { \\beta } = \\frac { 1 } { \\alpha \\beta } = \\frac { 1 } { 1 / 3 } = 3{/tex}.The equation of\xa0polynomial which has\xa0{tex}\\frac{1}{\\alpha} \\ and \\ \\frac{1}{\\beta}{/tex}as roots is\xa0{tex}y ^ { 2 } - \\frac { 7 } { 2 } y + 3 = \\frac { 1 } { 2 } \\left[ 2 y ^ { 2 } - 7 y + 6 \\right]{/tex} | |