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. State true or false and justify your answer.

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 with integral coefficients has integral roots.Justify your answer.

The quadratic equation 2x^(2) + x + 4 has ………real roots

State whether the following quadratic equations have two distinct real roots. Justicy your answer: x(1-x)-2=0

State whether the following quadratic equations have two distinct real roots. Justicy your answer: 2x^(2)+x-1=0

State whether the following quadratic equations have two distinct real roots. Justicy your answer: 3x^(2)-4x+1=0

State whether the following quadratic equations have two distinct real roots. Justicy your answer: x^(2)-3x+4=0

State whether the following quadratic equations have two distinct real roots. Justicy your answer: (x+1)(x-2)+x=0

State whether the following quadratic equations have two distinct real roots. Justicy your answer: (x-1)(x+2)+2=0

State whether the following quadratic equations have two distinct real roots. Justicy your answer: (x+4)^(2)-8x=0