Quadratic Equation | Lecture 02 | How to check if the given equation is Quadratic or not ? | Karan Soni

Quadratic Equations

Quadratic Equations

Which of the following is not a quadratic equation?

Which of the following is a quadratic equation?

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.

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

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.

If alpha and beta are the roots of the quadratic equation x^(2) + px + q = 0 , then form the quadratic equation whose roots are alpha + (1)/(beta), beta + (1)/(alpha)

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) .