Can a quadratic equation have two equal imaginary roots?

ax² + bx +c = 0; a,b,c are 'REAL' numbers; -b/a is the sum of roots and c/a is the product of roots. If a quadratic equation has two equal imaginary roots then there sum won't be a real number.( e.g. 2+3i + 2+3i = 4+6i). Their product may be a real number if the root is completely imaginary.(e.g. 3i * 3i = -9). read more

If a quadratic equation has two equal imaginary roots then there sum won't be a real number.( e.g. 2+3i + 2+3i = 4+6i). Their product may be a real number if the root is completely imaginary.(e.g. 3i * 3i = -9). read more

We know that two roots of quadratic equation are equal only if discriminant is equal to zero. Putting discriminant equal to zero, we get The basic definition of quadratic equation says that quadratic equation is the equation of the form , where . Therefore, in equation , we cannot have k =0. Therefore, we discard k=0. read more

Suppose the quadratic equation has 3(or any number greater than 2) roots. so we can factorise f(x) into [math]a (x - a_{1})(x - a_{2})(x - a_{3})[/math] where [math]a_{1}, a_{2},a_{3}[/math] are roots of the equation f(x)=0. But we can see the factorised polynomial is of degree 3 whereas the unfactorised one is of degree 2. So they can never be equal. read more