If −5 is one root of quadratic equation 2x2+px−15=0 and roots of quadratic equation p(x2+x)+k=0 is equal ,then find the value of k.
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Solution
Given, p(x2+x)+k=0 has equal roots so,b2=4ac px2+px+k=0 (p)2=4(p)(k) p=0,orp=4k and given -5 is root of 2x2+px−15=0 put x=−5 2(−5)2+(−5)p−15=0 50−5p−15=0 p=7 7=4k k=7/4