2x^(2)-2(2m+1)+m(m+1)=0

for what values of m, the equation 2x^(2) -2 ( 2m +1) x+ m ( m +1) = 0 m in R has (i) Both roots smallar than 2 ? (ii) Both roots greater than 2 ? (iii) Both roots lie in the interval (2,3) ? (iv) Exactly one root lie in the interval (2,3) ? (v) One root is smaller than 1, and the other root is greater than 1 ? (vi) One root is greater than 3 and the other root is smaller than 2 ? (vii) Roots alpha and beta are such that both 2 and 3 lie between alpha and beta ?

for what values of m, the equation 2x^(2) -2 ( 2m +1) x+ m ( m +1) = 0, m in R has (i) Both roots smallar than 2 ? (ii) Both roots greater than 2 ? (iii) Both roots lie in the interval (2,3) ? (iv) Exactly one root lie in the interval (2,3) ? (v) One root is smaller than 1, and the other root is greater than 1 ? (vi) One root is greater than 3 and the other root is smaller than 2 ? (vii) Roots alpha and beta are such that both 2 and 3 lie between alpha and beta ?

Absolute sum of integral values of m for which the equation (m^(2)+2m+1)x^(2)-2(m+1)x+(m+1)^(4)-9=0 has rational roots is

If m in Z and the equation m x^(2) + (2m - 1) x + (m - 2) = 0 has rational roots, then m is of the form

IF the roots of (3m +1) x^2 +2(m+1) x+m =0 are equal then m=

If y^(1//m)+y^(-1//m)=2x , then prove that (x^(2)-1)y_(2)+xy_(1)=m^(2)y^(2)

Number of integral values of m for which lines x+y+1=0,mx-m^(2)y+3=0 and 2mx-(2m-1)y+(3m+2)=0 are concurrent

Find the values of m for which the following equations have equal roots ? (3m+1)x^(2)+2(m+1)x+m=0

If equation x^2-(2+m)x+1(m^2-4m+4)=0 has coincident roots then (A) m=0, m=1 (B) m=0, m=2 (C) m=2/3, m=6 (D) m=2/3, m=1

If equation x^2-(2+m)x+1(m^2-4m+4)=0 has coincident roots then (A) m=0, m=1 (B) m=0, m=2 (C) m=2/3, m=6 (D) m=2/3, m=1