Quadratic Equation | Lecture 03 | Formation of Quadratic Equation | Karan Soni

Quadratic Equations

Quadratic Equations

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

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.

Let alpha and beta be the roots of the quadratic equation ax^(2)+bx+c=0, c ne 0, then form the quadratic equation whose roots are (1-alpha)/(alpha) and (1-beta)/(beta) .

If alpha, beta are the roots of the quadratic equation ax^(2) + bx + c = 0 then form the quadratic equation whose roots are palpha, pbeta where p is a real number.