Question

find a quadratic polynomial with rational coefficients whose one zero is√5-2.

Answer 1

well always remeber if one root is -2+√5
then other root is -2-√5
so the equation is in from
$x^{2} -( -2+\sqrt{5}-2- \sqrt{5} )x+( -2-\sqrt{5})( -2+\sqrt{5})=0 \\ x^{2} +4x-1$

Answer 2

Answer:

The quadratic polynomial is $x^{2}+4 x-1$

Step-by-step explanation:

The given one root is $-2+\sqrt{5}$

The given co-efficient of the “quadratic polynomial” is a rational number.

Then the another root is $-2-\sqrt{5}$

Sum of the roots$=(-2+\sqrt{5})+(-2-\sqrt{5})$

$\Rightarrow-4$

Product of the roots $=(-2+\sqrt{5}) \times(-2-\sqrt{5})$

$\Rightarrow 4+2 \sqrt{5}-2 \sqrt{5}-5$

$\Rightarrow-1$

Then, the quadratic equation becomes,

$=x^{2}- (\text {sum of the roots})+(\text {product of the roots})$

$=x^{2}-(-4) x+(-1)$

$\Rightarrow x^{2}+4 x-1$

Any polynomial with a degree of two is called as a quadratic polynomial. Such types of equations involving quadratic polynomials were called as quadratic equations.