Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

Let f(x)=x^2-2 p x+3 p^2-5 and g(x)=-x^2+2 p x+2 p-3 q, p, q R . If f(x) and g(x) do not intersects at two distinct points p R , then find the least value of q .

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aligned & x^2-2 p x+3 p^2-5=-x^2+2 p x+2 p-3 q & 2 x^2-4 p x+3 p^2-2 p+3 q-5=0 & D 0 & 2+6 p^2-4 2 (3 p^2-2 p+3 q-5 ) 0 &-p^2+2 p-3 q+5 0 & p^2-2 p+3 q-5 0 p R & D 0 4-4(3 q-5) 0 q 2 aligned

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