In a quadratic equation `ax^2 + bx+c= 0` if 'a' and 'c' are of opposite signs and 'b' is real, then roots of the equation are

If the roots alpha and beta (alpha+beta ne 0) of the quadratic equation ax^(2)+bx+c=0 are real and of opposite sign. Then show that roots of the equation alpha (x-beta)^(2)+beta(x-alpha)^(2)=0 are also real and of opposite sign.

The roots alpha and beta of the quadratic equation ax^(2)+bx+c=0 are real and of opposite sign.The roots of the equation alpha(x-beta)^(2)+beta(x-alpha)^(2)=0 are a.positive b. negative c.real and opposite sign d.imaginary

The quadratic equation ax^(2)+bx+c=0 has real roots if:

If the quadratic equation ax^(2)+bx+c=0 has real roots of opposite sign in the interval (-2,2), then prove that 1+(c)/(4a)-|(b)/(2a)|>0

Statement -1 : if a,b,c not all equal and a ne 0 ,a^(3) +b^(3) +c^(3) =3abc ,then the equation ax^(2) +bx+c=0 has two real roots of opposite sign. and Statement -2 : If roots of a quadractic equation ax^(2) +bx +c=0 are real and of opposite sign then ac lt0.

If one root of the quadratic equation ax^(2) + bx + c = 0 is 15 + 2sqrt(56) and a,b and c are rational, then find the quadratic equation.

In quadratic equation cx^(2) + bx + c = 0 find the ratio b : c if the given equation has equal roots

The roots of a quadratic equation ax^(2) + bx + c=0 are 1 and c/a , then a + b = "_____" .

The coefficients a, b and c of the quadratic equation, ax^(2) + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is: