Prove that `5x^2-8x+6` is always positive .

If x be real then prove that (x-1)(x-2)+1 is always positive.

If x is real and the roots of the equation ax^(2)+bx+c=0 are imaginary,then prove tat a^(2)x^(2)+abx+ac is always positive.

If x,y and z are three different numbers, then prove that : x^(2) + y^(2) + z^(2)- xy - yz- zx is always positive

If x is real, prove that the quadratic expression (i) (x-2)(x+3)+7 is always positive. (ii) 4x-3x^(2)-2 is always negative.

If x is real , show that (x-2)(x-3)(x-4)(x-5)+2 is always positive.

For what values of x , the expression x^2 - 5x + 6 is positive ?

Consider the following statements I.sin|x|+cos|x| is always positive.II.sin(x^(2))+cos(x^(2)) is always positive.

Prove that x^(2)+y^(2)+z^(2)-xy-yz-zx is always positive.

Find the values of x for which the expression x^(2)-(log_(5)2+log_(2)5)x+1 is always positive

Prove that sin 5 x cos 2x + cos 6 x sin 3 x = sin 8x cos x