Form the quadratic equation with rational coefficients if one of its roots be `2+sqrt3`

Form the quadratic equation with rational coefficients if one of its roots be -4+5i

Find the quadratic equation with rational coefficients if one of its roots be 3-sqrt5 .

Find the quadratic equation whose roots are given as -4 and 1/2 .

Find the quadratic equation whose roots are given below. sqrt 3 +sqrt 2, sqrt 3 - sqrt 2

Find the quadratic equation whose roots are given below. -3, 4/3

Find the quadratic equation whose roots are each less by 2 than the roots of the equation x^2- 16x+63 = 0.

Find the quadratic equation whose roots are given as sqrt2 +1 and sqrt2 -1 .

Find the nature of the roots of the following quadratic equations. If the real roots exist find them. x^2-2sqrt(3x)-9=0

Find the nature of the roots of the following quadratic equations.If the real roots exist,find them:(ii) 3x^2-4sqrt3x+4=0

Solve the following quadratic equation by the method of completing square:(viii) x^2-(sqrt3+1)x+sqrt3=0