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if -5 is a root of the quadratic equation 2x2+px-15=0 and thequadratic equation p(x2+x)+k=0 has equal roots,find the value of k

if -5 is a root of the quadratic equation 2x2+px-15=0 and thequadratic equation p(x2+x)+k=0 has equal roots,find the value of k

Grade:10

1 Answers

Yogesh Kumar
43 Points
3 years ago
-5 is one root of the equation 2x2+px-15=0 so it will satisfy this equation.
Put x=-5
we get, 50-5p-15=0
or p=7 
Now p(x2+x)+k=0
or 7x2+7x+k=0
Now as the equation has equal roots its discriminant should be 0
D=0 or b2-4ac=0
or 49-4(7)k=0
or 7-4k=0 or k=7/4

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