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.

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

Prove that both the roots of the equation (x-a)(x-b)+ (x-b)(x-c)+(x-a)(x-c)=0 are real.

If roots of equation x^(2)-2cx+ab=0 are real and unequal,then prove that the roots of x^(2)-2(a+b)x+a^(2)+b^(2)+2c^(2)=0 will be imaginary.

If the roots of (a-b)x^(2)+(b-c)x+(c-a)=0 are real and equal, then prove that b, a, c are in arithmetic progression.

If roots of equation x^2-2c x+a b=0 are real and unequal, then prove that the roots of x^2-2(a+b)x+a^2+b^2+2c^2=0 will be imaginary.

If roots of equation x^2+2c x+a b=0 are real and unequal, then prove that the roots of x^2-2(a+b)x+a^2+b^2+2c^2=0 will be imaginary.

If roots of equation x^2-2c x+a b=0 are real and unequal, then prove that the roots of x^2-2(a+b)x+a^2+b^2+2c^2=0 will be imaginary.