Quadratic Equation | Lecture 08 | Examples on Quadratic Formula | Karan Soni

Quadratic Equations

Quadratic Equations

Solve the following quadratic equation using the Standard Quadratic Formula 3x ^2 + 5x - 9 = 0

Find the roots of the following quadratic equations, if they exist, using the quadratic formula: (i) 3x^2-5x+2=0 (ii) x^2+4x+5=0 (iii) 2x^2-2sqrt(2)x+1=0

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 roots of the quadratic equations by applying the quadratic formula. (i) 2x^2 -7x+3 =0 (ii) 2x^2+x-4 =0 (iii) 4x^2+4sqrt3x+3=0 (iv) 2x^2+x+4 = 0

If A.M. and GM. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.

If A.M. and GM. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.

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

Find the roots of the quadratic equations by using the quadratic formula 1/2 x^(2)-sqrt(11)x+1=0