[" Roots "ax^(2)+bx+c=0" are real and dif- "],[" ferent if "]

IF the roots of the equation ax ^2 +bx + c=0 are real and distinct , then

If the roots of the equation ax^(2)+bx+c=0 are real and distinct,then

The roots of ax^(2)+bx+c=0, ane0 are real and unequal, if (b^(2)-4ac)

If the roots of a quadratic equation ax^(2) + bx + c = 0 are real and equal then b^(2) =…

Prove that the roots of ax^2+2bx+c=0 will be real and distinct if and only if the roots of (a+c) (ax^2+2bx+c) =2 (ac-b^2) (x^2+1) are imaginary

If coefficients of the equation ax^(2)+bx+c=0,a!=0 are real and roots of the equation are non-real complex and a+c

Prove that the roots of ax^(2)+2bx + c = 0 will be real distinct if and only if the roots of (a+c)(ax^(2)+2bx + c)=2(ac-.b^(2))(x^(2)+1) are imaginary.

Theorem : Let a, b, c in R and a ne 0. Then the roots of ax^(2)+bx+c=0 are non-real complex numbers if and only if ax^(2)+bx+c and a have the same sign for all x in R .