Find p which (p+1)x square - 6(p+1)x + 3(p+q) = 0 has equal roots . Also find roots.

Find p which (p+1)x square - 6(p+1)x + 3(p+q) = 0 has equal roots . Al

1.	Find p which (p+1)x square - 6(p+1)x + 3(p+q) = 0 has equal roots . Also find roots.
Answer» The correct equation is {tex}\\left( {p + 1} \\right){x^2} - 6\\left( {p + 1} \\right)x + 3\\left( {p + 1} \\right) = 0{/tex}Here a = p + 1, b = -6(p + 1), c = 3(p + 1)For equal root,\xa0{tex}{b^2} - 4ac = 0{/tex}=> {tex}{\\left[ { - 6\\left( {p + 1} \\right)} \\right]^2} - 4 \\times \\left( {p + 1} \\right) \\times 3\\left( {p + 1} \\right) = 0{/tex}=> {tex}36\\left( {{p^2} + 1 + 2p} \\right) - 12\\left( {{p^2} + 1 + 2p} \\right) = 0{/tex}=> {tex}3\\left( {{p^2} + 1 + 2p} \\right) - \\left( {{p^2} + 1 + 2p} \\right) = 0{/tex}=> {tex}3{p^2} + 3 + 6p - {p^2} - 1 - 2p = 0{/tex}=> {tex}{p^2} + 4p + 2 = 0{/tex}=> {tex}p = {{ - 4 \\pm \\sqrt {16 - 8} } \\over 2}{/tex}=> {tex}p = {{ - 4 \\pm 2\\sqrt 2 } \\over 2}{/tex}=> {tex}p = - 2 \\pm \\sqrt 2 {/tex}