First slide
Theory of equations
Question

If the quadratic equations, x2+bx+c=0 and bx2+cx+1=0 have a common root then

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Solution

Equations x2+bx+c=0 and bx2+cx+1=0 have a common root.

(bc1)2=cb2bc2b2c2+12bc=bcb3c3+b2c21+c3+b3=3bc(1+c+b)c2+b2+1bcbc=0b+c+1=0 and c2+b2+1=c+b+bc

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