If -5 is a root of the quadratic equation 2x^2+px-15=0 and the quadratic equation p(x^2+x)+k=0 has equal roots, then find the values of p and k.
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2x^2+px-15=0
p (x^2+x)+k=0
since -5 is the root of both equations
2 (-5)^2+p(-5)-15=0
50-5p-15=0
5p=35
p=7
In equation (II)
7 [(-5)^2 +(-5)]+k=0
7(20)+k=0
140+k=0
k=-140
so k=-140. & p=7
p (x^2+x)+k=0
since -5 is the root of both equations
2 (-5)^2+p(-5)-15=0
50-5p-15=0
5p=35
p=7
In equation (II)
7 [(-5)^2 +(-5)]+k=0
7(20)+k=0
140+k=0
k=-140
so k=-140. & p=7
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