Question

prove that if the coefficient of x square and the constant term of an quadratic equation has opposite signs then the quadratic equation has real roots ​

Answer 1

Answer:

Step-by-step explanation

Hello,

         We know that for a quadratic equation to have real roots, the value of the discriminant must be greater than zero.

                    For the quadratic equation ax^2+bx+c,

                              discriminant= (b^2)-4ac

                       For real roots, this must be positive.

     Given that the coefficient of x square and the constant term have opposite signs. This implies their product is negative.

                      So, ac=-ve

                     This implies (b^2)-4ac is (b^2)-4(-ve)

                                                                =(b^2)+4(+ve)

                                                                =(positive)+4(positive)

                                                                =positive

       So, discriminant of such a quadratic is positive which implies that it has real roots.

                                   Hence Proved.