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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.

Posted by Sahitha?? Sharma 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Since (-5) is a root of given quadratic equation 2x² + 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 {tex}p \left( x ^ { 2 } + x \right) + k = 0{/tex} has equal roots

{tex}p x ^ { 2 } + p x + k = 0{/tex}

So {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}

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