Question

If one zero of the polynomial 2 − 4 + 1 is 2 + √3, find the other zero.

Steps pls

Answer 1

Answer:

$x = 2 - 4 + 1$

$one \: zero(0) \: = 2 + \sqrt{3}$

Let α = 2 + √3 and β be the other zero.

As we know, it's a quadratic equation, so it should have maximum two zeros.

By using the relationship between the co-efficients and the zeros of a quadratic equation,

$\alpha + \beta = - \frac{b}{a}$

$(2 + \sqrt{3} ) + \beta = \frac{ - ( - 4)}{1}$

$(2 + \sqrt{3} ) + \beta = \frac{4}{1}$

$\sqrt{3} + \beta = \frac{4}{1} - 2$

$\sqrt{3} + \beta = \frac{2}{1}$

$\beta = 2 - \sqrt{3}$

$so, \: the \: other \: zero(0) \: is \: 2 - \sqrt{3}$