Quadratic Equation | Lecture 10 | Examples on Nature of Roots | Karan Soni

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

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.

Find the quadratic equation whose roots are the reciprocals of the roots of the equation x^(2) - cx + b = 0

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

The coefficient of x in a quadratic equation x^2 + px +q=0 was taken as 17 in place of 13 and its roots found to be -3 and -10 . The roots of the original equation are

Statement -1 : There is just on quadratic equation with real coefficients, one of whose roots is 1/(3+sqrt7) and Statement -2 : In a quadratic equation with rational coefficients the irrational roots occur in pair.

Statement -1 : There is just one quadratic equation with real coefficient one of whose roots is 1/(sqrt2 +1) and Statement -2 : In a quadratic equation with rational coefficients the irrational roots are in conjugate pairs.

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

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