Quadratic Equation | Lecture 09 | Nature of Roots | Karan Soni

Find a quadratic equation for which the sum of the roots is 7 and the sum of the squares of the roots is 25.

Form quadratic equation whose roots are : 2,5

Write whether the following statements are true or false. Justify your answers. (i) Every quadratic equation has exactly one root. (ii) Every quadratic equation has atleast one real root. (ii) Every quadratic equation has atleast two roots. (iv) Every quadratic equations atmost two roots. (v) If he coefficient of x^(2) and the constnat term of a quadratic equation have opposite sigh, then the quadratic equation has real roots. (vi) If the coefficient of x^(2) and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

The quadratic equation whose roots are reciprocal of the roots of the equation ax^(2) + bx+c=0 is :

Find the quadratic equation whose sum of the roots is 2 and sum of the cubes of the roots is 27.

If (1 - p) is a root of quadratic equation x^(2) + px + (1- p)=0 , then its roots are

Find the discriminant of the quadratic equation 2x^2-4x+3=0 , and hence find the nature of its roots.

A quadratic equation is chosen from the set of all quadratic equations which are unchanged by squaring the roots. The chance that the chosen equation has equal root, is