If -5 is a root of (2x^2+px-15)=0 and roots of p(x^2+x)+k=0 are equal,then find p and k.

If -5 is a root of (2x^2+px-15)=0 and roots of p(x^2+x)+k=0 are equal,

1.	If -5 is a root of (2x^2+px-15)=0 and roots of p(x^2+x)+k=0 are equal,then find p and k.
Answer» Since (-5) is a root of given quadratic equation\xa02x2 + px + 15 =0,then,{tex}2 ( - 5 ) ^ { 2 } + p ( - 5 ) - 15 = 0{/tex}{tex}50 - 5 p - 15 = 0{/tex}{tex}5 p = 35 \\Rightarrow p = 7{/tex}Now\xa0{tex}p \\left( x ^ { 2 } + x \\right) + k = 0{/tex}\xa0has equal roots\xa0{tex}p x ^ { 2 } + p x + k = 0{/tex}So\xa0{tex}( b ) ^ { 2 } - 4 a c = 0{/tex}{tex}( p ) ^ { 2 } - 4 p \\times k = 0{/tex}{tex}( 7 ) ^ { 2 } - 4 \\times 7 \\times k = 0{/tex}28k = 49{tex}k = \\frac { 49 } { 28 } = \\frac { 7 } { 4 }{/tex}hence p = 7 and {tex}k = \\frac { 7 } { 4 }{/tex}