If one root of a quadratic equation with rational coefficients is √3+2, then the quadratic equation is

Question

If one root of a quadratic equation with rational coefficients is √3+2, then the quadratic equation is (A) x2+4 x+1=0 (B) x2-4 x-1=0 (C) x2-4 x+1=0 (D) x2+4 x-1=0

Tardigrade Admin · Accepted Answer

α=√3+2 b =-√3+2 P =α β=1 S =α+β=4 ⇒ text quadratic equation is x 2-4 x +1=0

Q. If one root of a quadratic equation with rational coefficients is $3 + 2$ , then the quadratic equation is

$x^{2} + 4 x + 1 = 0$

$x^{2} - 4 x - 1 = 0$

$x^{2} - 4 x + 1 = 0$

$x^{2} + 4 x - 1 = 0$

$α = 3 + 2$
$b = - 3 + 2$
$P = α β = 1$
$S = α + β = 4$
$\Rightarrow quadratic equation is x^{2} - 4 x + 1 = 0$

Q. If one root of a quadratic equation with rational coefficients is 3​+2, then the quadratic equation is

x2+4x+1=0

x2−4x−1=0

x2−4x+1=0

x2+4x−1=0