Question

0.85. The number of roots common between the two equations x + 3x2 + 4x + 5 = 0 and x + 2x2 + 7x+3=0 is: (a) o (b) 1 (c) 2 (d) 3

MBA Exams

Maths

Solution

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Considering [ begin{array}{l} f(x)=x^{3}+3 x^{2}+4 x+7 g(x)=x^{3}+2 x^{2}+7 x+5 end{array} ] you could notice that their derivatives never cancel in the real domain. So, ( f(x)=0 ) has only one real root and same for ( g(x)=0 . ) So, the maximum number of common roots is ( 1 . ) Now, inspection: ( f(-3)=-5, f(-2)=3 ; ) so the root for ( f(x)=0 ) is somewhere between -3 and -2 ( g(-1)=-1, g(0)=5 ; ) so the root for ( g(x)=0 ) is somewhere between -1 and 0 So, no common root.