∫ax+b/√px2+qx+r dx Form and Integration by Parts

∫ax+b/√px2+qx+r dx Form || Integration By Parts

If the roots of x^(3)+px^(2)+qx+r=0 are in GP find the relation between p,q and r

If the roots of the equation px^(2)+qx+r=0 are in the ratio l:m then

0:7Let p, q, r e R such that 3qgtp2. Then the function g: RR given by g(x)= x3 + px2 + qx +r, is(A) one-one and onto(B) onto but not one-one(C) one-one but not onto(D) neither one-one nor onto

Illustration Based upon ∫(√ ax2+bx+c )dx ||Illustration Based upon ∫(px+q)(√ax2+bx+c) dx || Illustration Based upon ∫(px2+qx+r)/(ax2+bx+c) dx

If alpha,beta are the roots of the equation px^(2)-qx+r=0, then the equation whose roots are alpha^(2)+(r)/(p) and beta^(2)+(r)/(p) is (i) p^(3)x^(2)+pq^(2)x+r=0 (ii) px^(2)-qx+r=0 (iii) p^(3)x^(2)-pq^(2)x+q^(2)r=0 (iv) px^(2)+qx-r=0

If p, q, r are positive and are in AP, the roots of quadratic equation px^(2) + qx + r = 0 are real for :