Quadratic equation when one root is given

The quadratic equation whose one root is - (i)/(4) :

Find the quadratic equation whose one root is (1-i) .

The quadratic equation whose one root is (-3+ i sqrt7)/(4) is

The quadratic equation whose one root is (3+sqrt(5))/(2-sqrt(5)) is

If alpha is one of the non real imaginary seventh roots of unity, then form the quadratic equation whose roots are given by alpha + alpha^(2) + alpha^(4) and alpha^(3) + alpha^(5) + alpha^(6)

Form a quadratic equation whose roots are -4a n d6.

Form a quadratic equation whose roots are -4a n d6.

Find the quadratic equation whose sum of the roots is 2 and sum of the cubes of the roots is 27.

Form quadratic equation whose roots are : 2,5

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.