" 8.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

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 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

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.

If roots of equation x^3-2c 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.