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 qx^(2)+2px+2q=0 are real and unequal, prove that the roots of the equation (p+q)x^(2)+2qx+(p-q)=0 are imaginary.

If the roots of the equation ax^2 +x+b=0 be real, and unequal then the roots of the equation x^2-4sqrt(ab)x + 1 = 0 will be

If the roots of the equation qx^2+2px+2q=0 are real and unequal, prove that the roots of the equation (p+q)x^2+2qx+(p-q)=0 are imaginary.

If the roots of the equation qx^2 + 2px + 2q =.0 are real and unequal then prove that the roots of the equation (p + q)x^2 + 2qx + (p - q)=0 are imaginary,

IF the roots of the equation px^2-2qx+p=0 are real and unequal, show that the roots of the equation qx^2-2px+q=0 are imaginary (both p and q are real).

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^2-2c 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.