[" 41.Show that if "x" is real and "x^(2)+5<6x," then "x" must lie "],[" between "1" and "5.]

Show that if x is real and x^2+5lt6x , then x must lie between 1 and 5.

If x be real then 2x^(2)+5x-3>0 if

If x is a real number and |x| =5 b.-5

If alpha and beta be the roots of the equation 5x^2+bx+c=0 Show that 5x^2+bx+c=5(x-alpha)(x-beta) Show also that for all real values of x the expression 5x^2+bx+c cannot be negative if alpha and beta are real and equal

If alpha and beta be the roots of the equation 5x^2+bx+c=0 Show that 5x^2+bx+c=5(x-alpha)(x-beta) Show also that for all real values of x the expression 5x^2+bx+c cannot be negative if alpha and beta are conjugate complex.

Use contradiction method to show the validity of the following statement : If x is real number with xgt5 , " then " x^(2)gt25 .

If x is real and (x^2+2x+c)//(x^2+4x+3c) can take all real values, of then show that 0lt=clt=1.

If x is real and (x^(2)+2x+c)/(x^(2)+4x+3c) can take all real values,of then show that 0<=c<=1

If x is real and (x^2+2x+c)/(x^2+4x+3c) can take all real values, of then show that 0lt=clt=1.

If x is real and (x^2+2x+c)//(x^2+4x+3c) can take all real values, of then show that 0lt=clt=1.