" 1."x^(2)-6x+3=0

Find the greatest and least value of y= x^(3)-3x^(2) + 6x-2 on [-1,1] y is differentiable function of x and y'(x) = 3x^(2) -6x + 6= 3(x^(2) -2x+2) =3(x-1)^(2) gt 0 .

A: The equation whose roots are the reciprocals of the roots of 2x^(3) + 7x^(2) - 6x + 1 = 0 is x^(3) - 6x^(2) + 7x + 2 =0 . R: the equation whose roots are the reciprocals of those of f(x) = 0 is f(1/x) = 0.

x_1 and x_3 are the roots of the equation Ax ^2 - 4x +1=0 and x_2 and x_4 =0 are the roots of the requation Bx^2 - 6x + 1=0 if x_1 , x_2 , x_3 ,x_4 form a H.P , then (A,B) =

Find the sets which are equal, from the following sets : A = {2,1,3} B = {x : x^(3) - 6x^(2)+11x - 6 = 0} C = {0,1},D={a,b} E = {x : x^(2) - x=0} F = {x : (x-a)(x-b)=0} .

Which of the following are quadratic equations? x^(2)+6x-4=0( ii) sqrt(3)x^(2)-2x+(1)/(2)=0 (iii) x^(2)+(1)/(x^(2))=5

Consider the following sets. I. A={1,2,3} II. B={x inR:x^(2)-2x+1=0} III. C={1,2,2,3} IV. D={x inR:x^(3)-6x^(2)+11x-6=0} Which of the following are equal?

Which of the following sets are equal? (i) A={1,2,3} (ii) B={x in R:x^(2)-2x+1=0} (iii) C={1,2,2,3} (iv) D={x in R:x^(3)-6x^(2)+11x-6=0}

Prove that function f(x) = {-2x^(3)+3x^(2)-6x+5,xlt0 -x^(2)-x+1, xge0 is decreasing for all x.