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  4. The coefficient of x in x2+px+q=0 was taken as 17 in place of 13 and its roots were found to be -2 and -15 The roots of the original equation are:

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Q. The coefficient of $ x $ in $ {{x}^{2}}+px+q=0 $ was taken as 17 in place of 13 and its roots were found to be $ -2 $ and $ -15 $ The roots of the original equation are:

KEAMKEAM 2003

Solution:

The given equation is $ {{x}^{2}}+17x+q=0 $ $ \therefore $ Product of roots $ =(-2)(-15)=q $ $ \Rightarrow $ $ q=30 $ $ \therefore $ Original equation is $ {{x}^{2}}+13x+30=0 $ $ \Rightarrow $ $ {{x}^{2}}+10x+3x+30=0 $ $ \Rightarrow $ $ (x+10)(x+3)=0 $ $ \Rightarrow $ $ x=-10,-3 $