Target Audience: High School Students, College Freshmen and Sophomores, Class 11/12 Students in India preparing for ISC/CBSE and Entrance Examinations like the IIT-JEE , and anyone else who needs this Tutorial as a reference!
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Quadratic inequalities refer to the inequalities of the type: ax2+bx+c>0 or ax2+bx+c<0 (or with the inequalities with the equal to sign)
The basic concepts in inequalities are:
Using this, if we have factorized the expression in the form: (x-p)(x-q),and p<q, then : if (x-p)(x-q)>0 then either x-p>0 and x-q>0 or x-p<0 and x-q<0
=>x>p and x>q or x<p and x<q
=>x>q or x<p (Because if x>p and x>q, then x>q is the common solution as p<q(Notice that “and”
leads to taking the common solution, and “or” leads to unifying the solutions) )
Similarly, if (x-p)(x-q)<0 then, p<x<q.
Clearly, when x<α and when x>β, we have a positive value of f(x), where f(x)= ax2+bx+c when α<x< β, we have a negative value of f(x)
Q: Solve x2+x+1<0
Q: Solve x2+4x>0
Q: Solve x2+5x+1>0.
Q: Solve x2+11x+24<0
Q: If x2+kx+2=0 has real roots, what can be the possible values of k?
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