Let `p,q,r in R` such that `3q>p^2`. Then the function `g:R->R` given by `g(x)=x^3+px^2+qx+r`, is

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

Let f : R rarr R be a function given by f(x) = px +q AA x in R . Find constants p and q such that fof = I_(R)

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in H.P 2p^3 =9r (pq-3r)

show that the condition that the roots of x^3 + px^2 + qx +r=0 may be in G.P is p^3 r=q^3

show that the condition that the roots of x^3 + px^2 + qx +r=0 may be in G.P is p^3 r=q^3

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in G.P p^3 r= q^3

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in H.P then 2q^3 =9r (pq-3r)

If p, q, r each are positive rational number such tlaht p gt q gt r and the quadratic equation (p + q - 2r)x^(2) + (q + r- 2p)x + (r + p - 2q) = 0 has a root in (-1 , 0) then which of the following statement hold good? (A) (r + p)/(q) lt 2 (B) Both roots of given quadratic are rational (C) The equation px^(2) + 2qx + r = 0 has real and distinct roots (D) The equation px^(2) + 2qx + r = 0 has no real roots

If p, q, r each are positive rational number such tlaht p gt q gt r and the quadratic equation (p + q - 2r)x^(2) + (q + r- 2p)x + (r + p - 2q) = 0 has a root in (-1 , 0) then which of the following statement hold good? (A) (r + p)/(q) lt 2 (B) Both roots of given quadratic are rational (C) The equation px^(2) + 2qx + r = 0 has real and distinct roots (D) The equation px^(2) + 2qx + r = 0 has no real roots

Given that q^2-p r 0, then the value of {:|(p, q, px+qy), (q, r, qx+ry), (px+qy, qx+ry, 0) |:} is- a. zero b. positive c. negative \ d. q^2+p r