Question

find the zeros of the polynomial x square - 3 and verify the relationship between the zeros and coefficients

Answer 1

Thus so

The polynomial is

➡ X² - 3 = 0
. X² - 0X - 3 = 0
. X² - ROOT 3 + ROOT 3 - 3 = 0
. X ( X + ROOT 3 ) - ROOT 3 ( X + ROOT 3 )

➡ X = - ROOT 3 @
➡ X = + ROOT 3. ₹

THUS AS @ + ₹ = 0
. - B / A = 0

. AS @ * ₹ = -3
. C / A = -3 / 1 = -3

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Answer 2

Answer:

Given quadratic equation,

$x^2-3$

Let, $f(x) = x^2 - 3$

For zeroes,

$f(x) = 0$

$x^2-3=0$

$x^2=3$

$x=\pm \sqrt{3}$

Thus, the zeroes of the given equation are √3 and -√3,

Since, for a quadratic equation,

$\text{Sum of zeroes}=-\frac{\text{Constant term}}{\text{Coefficient of } x^2}$

$\text{Product of zeroes}=\frac{\text{Constant term}}{\text{Coefficient of } x}$

Verification :

$\sqrt{3}-\sqrt{3}=0$

$\sqrt{3}\times \sqrt{3}=3$