Solve the quadratic inequalities, x2 + x – 6 ≥ 0.
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the given question is x^2+x-6>0
then,by factorization method,we have
=> x^2+x-6>0
=>x^2+3x-2x-6>0
=>x(x+3)-2(x+3)>0
=>(x+3)(x-2)>0
=>(x+3)>0 or (x-2)>0
=>x>-3 or x>2...
and Now,by Shridharacharya formula, we have
=>x^2+x-6>0
a=1, b=1 and c=(-6) then,
D=(b^2-4ac)
=(1^2-4.1.(-6)
=(1+24)=25.
now,x = -b(+-)√D/2a
=> -1(+-)√25/2.1.
=> -1(+-)5/2
=> now,+area =(-1+5)/2 => 4/2
=>x=2....
and,now - area =(-1-5)/2=>-6/2.
=>x=-3....
Hence,proved..
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