First slide
Theory of expressions
Question

If the equation ax2+bx+c=0,a,b,cR have non-real roots, then

Moderate
Solution

Since the roots of ax2 + bx + c = 0 are nonreal, so, f(x) = ax2 + bx + c will have same sign for every value of x. Hence,

    f(0)=c,f(1)=a+b+c,f(1)=ab+c    f(2)=4a2b+c     c(a+b+c)>0,c(ab+c)>0,c(4a2b+c)>0

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