Question

6. Find the zeroes of the polynomial x² – 3 and verify the relationship between the zeroes and the
coefficients.​

Answer 1

Step-by-step explanation:

${x}^{2} - 3 = 0$

${x}^{2} = 3$

x = ±√3

Now let α = √3 and ß = -√3

We know that,

$α + ß = \frac{ - b}{a}$

$αß = \frac{c}{a}$

Here a = 1 (coefficient of x²), b = 0 (coefficient of x) and c = -3 (constant)

$α + ß = \frac{ - b}{a}$

$\sqrt{3} + - \sqrt{3} = \frac{ - 0}{1}$

$0 = 0$

$αß = \frac{c}{a}$

$\sqrt{3} \times - \sqrt{3} = \frac{ - 3}{1}$

$- 3 = - 3$

$∴verified$