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| 1. |
If p,q are zeroes of polynomials 2x\'2-x+3,find the value of p\'2 and q\'2 |
| Answer» we have f(x) = 2x2\xa0- 7x +3{tex}\\Rightarrow{/tex}\xa0Sum of roots = p + q =\xa0{tex}- \\frac { \\text { Coefficient of } x } { \\text { Coefficient of } x ^ { 2 } }{/tex}=\xa0{tex}- \\left( \\frac { - 7 } { 2 } \\right) = \\frac { 7 } { 2 }{/tex}{tex}\\Rightarrow{/tex}\xa0Product of roots = pq =\xa0{tex}{/tex}{tex}\\frac { \\text { Constant term } } { \\text { Coefficient of } x ^ { 2 } } = \\frac { 3 } { 2 }{/tex}Since, {tex}(p+q)^2{/tex}\xa0= p2\xa0+ q2\xa0+ 2pq{tex}\\Rightarrow{/tex}\xa0p2\xa0+ q2\xa0= (p + q)2\xa0- 2pq{tex}= \\left( \\frac { 7 } { 2 } \\right) ^ { 2 } - 3 = \\frac { 49 } { 4 } - \\frac { 3 } { 1 } = \\frac { 37 } { 4 }{/tex}Hence, the value of {tex}p^2+q^2{/tex}=\xa0{tex}\\frac{37}{4}{/tex} | |