a polynomial of an even degree has atleast two real roots if it attains atleast one value opposite in sign to the coefficient of its highest-degree term.

Show that a polynomial of an odd degree has at least one real root.

A polynomial of degree n can have atmost n real roots

For an even degree reciprocal equation of class two root (s) are

f(x)g(x)=0 where f(x) and g(x) are degree 2 polynomial with sum of zeroes -2 and +2 respectively.These constant terms is same as well as coefficient of highest degree term, then number of coincident zeroes of their product is (A)1 (B) 2 (C) 3(D) none of these

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.

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.

Show x^5-2x^2+7 =0 has atleast two imaginary roots.

The polynomial equation of degree 4 having real coefficients with three of its roots as 2 pm sqrt3 and 1+2i is

Find a polynomial equation of minimum degree with rational coefficients, having 2i+3 as a root.

Find a polynomial equation of minimum degree with rational coefficients , having 2+sqrt3 as a root.