Question

please solve this question ​

Answer 1

$\huge{ \underline{ \sf{ \blue{Detailed \: AnsweR\::}}}}$

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Given Equation : x² - 3

‍ ‍ ‍ ‍ ‍ ‍= x² + 0x - 3

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To Find : The zeroes of the given polynomial.

In the equation x² + 0x - 3,

$\boxed{ \blue{a = 1}}$

$\boxed{ \green{b = 0}}$

$\boxed{ \purple{c = - 3}}$

We know that, the sum of the zeroes, i.e

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

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

And the product of zeroes, i.e

$\alpha \times \beta = \frac{c}{a}$

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

Now simplifying the given polynomial,

x² - 3 = 0

x = ±√3

$\sf{Verifying\:The\: Relationship\: Between\: Zeroes\:And\: Coefficients}$

Let us take $\alpha$ as 3

And let us take $\beta$ as -3

Now,

$\alpha + \beta = \sqrt{3} + ( - \sqrt{3} ) = 0$

$\alpha \times \beta = \sqrt{3} \times - \sqrt{3} = - 3$

Hence Relation Verified!