" 1.If Show that the roots of "(x-a)(x-b)=h^(2)" are always real."

Prove that the roots of (x-a)(x-b)=h^(2) are always real.

If a,b, are real, then show that the roots of the equation (x-a)(x-b) = b^2 are always real.

Show that the roots of (x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0 are real, and that they cannot be equal unless a=b=c.

If the roots of ax^(2)+x+b=0 be real and unequal, show that the roots of (x^(2)+1)/(x)=4sqrt(ab) are imaginary.

The roots of (x-a)(x-b)=abx^(2)( a) are always real (c) are real and equal if and only if a=b( b)may be complex depending upon a (d)are real and distinct if and only if a!=0

IF a,b,c are real, prove that the roots of the equation 1/(x-a)+1/(x-b)+1/(x-c)=0 are always real and cannot be equal unless a=b=c.

-If a,b,c in R then prove that the roots of the equation 1/(x-a)+1/(x-b)+1/(x-c)=0 are always real cannot have roots if a=b=c

Show that the roots of the equation x^(2)+px-q^(2)=0 are real for all real values of p and q.

If x is real , show that the expressions (x^2-ab)/(2x-a-b) has no real value between a and b.

-If a,b,c in R then prove that the roots of the equation (1)/(x-a)+(1)/(x-b)+(1)/(x-c)=0 are always real cannot have roots if a=b=c