which one of the following sets has elements as odd positive integers (a) `S={x in R|x^3-8x^2+19x-12=0}` b) `S={x in R|x^3-9x^2+23x-15=0}` c) `S={x in R|x^3-7x^2+14x-8=0}` d) `S={x in R|x^3-12x^2+44x-48=0}`

Solve : x^3-8x^2+19x-12=0

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}

Which of the following equations has 2 as a root? (a) x^(2)-4x+5=0 , (b) x^(2)+3x-12=0 (c) 2x^(2)-7x+6=0 , (d) 3x^(2)-6x-2=0

Decide, among the following sets, which sets are subsets of one and another: A = { x : x in R and x^2- 8x + 12 = 0 } , B = { 2, 4, 6 }, C = { 2, 4, 6. 8 ......}

Which of the following quadratic equations has roots 3, 5? a) x^2-15x+3=0 b) x^2-8x+15=0 c) x^2+3x+5=0 d) x^2+8x-15=0

Determine if the set A ={-1,1,3}is a proper subset of the set B= {x:x in R and x^3-2x^2-x+2=0}

Express each of the following sts as an interval : (i) A={x:x in R, -4 , lt x lt 0} (ii) B={x:x in R, 0 le x lt 3} (iii) C= {x:x in R, 2 lt x le 6} (iv) D= {x:x in R, -5 le x le 2 } (v) E= {x:x in R, -3 le x lt2) (vi) F={x:x in R, -2, le x lt 0}

Analyze the roots of the following equations: (i) 2x^(3) - 9x^(2) + 12x - (9//2) = 0 (ii) 2x^(3) - 9x^(2) + 12x - 3 = 0

In Delta ABC the roots of the equation x^3-(r+4R)x^2+s^2x-s^2r=0 are