The equation `ax^(2)+6x-9=0` will have imaginary roots if

If 0 lt a lt b lt c and the roots alpha, beta of the equation ax ^(2)+bx+c=0 are imaginary, then

If 0

If x is real and the roots of the equation ax^(2)+bx+c=0 are imaginary,then prove tat a^(2)x^(2)+abx+ac is always positive.

If the roots of the equation ax^(2) - 4x + a^(2) = 0 are imaginary and the sum of the roots is equal to their product, then a^(-)

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has only purely imaginary roots at real roots two real and purely imaginary roots neither real nor purely imaginary roots

If roots of the equation ax^(2)+2(a+b)x+(a+2b+c)=0 are imaginary then roots of the equation ax^(2)+2bx+c=0 are

If 1 is the root of the quadratic equation 3x^(2)+ax-2=0 and the quadratic equation a(x^(2)+6x)-b=0 has equal roots, find 'b'.

Assertion : 4x^(2) - 12x + 9 = 0 has repeated roots. Reason : The quadratic equation ax^(2) + bx + c = 0 have repeated roots if D gt 0 .

Assertion (A) : The roots of the quadratic equation x^(2)+2x+2=0 are imaginary. Reason (R ) : If discriminant D=b^(2)-4ac lt 0 then the roots of the quadratic equation ax^(2)+bx+c=0 are imaginary.