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.

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 the equation x^2+x+a=0 be real and unequal, then prove that the roots of the equation 2x^2-4(1+a)x+2a^2+3=0 are imaginary (a is real).

If the roots of the equation x^2+2c x+a b=0 are real unequal, prove that the equation x^2-2(a+b)x+a^2+b^2+2c^2=0 has no real roots.

If the roots of the equation x^2+2c x+a b=0 are real and unequal, then the roots of the equation x^2-2(a+b)x+(a^2+b^2+2c^2)=0 are: (a) real and unequal (b) real and equal (c) imaginary (d) rational

If the roots of the equation , x^2+2c x+ab=0 are real and unequal, then the roots of the equation, x^2-2(a+b)x+(a^2+b^2+2c^2)=0 are: a. real and unequal b. real and equal c. imaginary d. Rational

If roots of equation a-b)x^(2)+(b-c)x+(c-a)=0 are equal then prove that b+c=2a

If the roots of the equation x^(2)+2cx+ab=0 are real and unequal,then the roots of the equation x^(2)-2(a+b)x+(a^(2)+b^(2)+2c^(2))=0 are: (a) real and unequal (b) real and equal (c) imaginary (d) rational