Question

Find the polynomial of the zeroes √3 , -√3

Answer 1

✯✯ QUESTION ✯✯

Find the polynomial of the zeroes √3 , -√3..

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✰✰ ANSWER ✰✰

$\longmapsto\tt{Zeroes\:are=\sqrt{3}\:and\sqrt{-3}}$

$\longmapsto\tt{\alpha+\beta=\sqrt{3}}$

$\longmapsto\tt{\alpha\beta=\sqrt{-3}}$

➥Using Formula : -

$\longmapsto\tt{\small{\boxed{\bold{\bold{\orange{\sf{{x}^{2}-(\alpha+\beta)x+\alpha\beta}}}}}}}$

➥Putting Values : -

$\longmapsto\tt{{x}^{2}-\sqrt{3}x+\sqrt{(-3)}}$

$\longmapsto\tt{{x}^{2}-\sqrt{3}x-\sqrt{3}}$

So, The quadratic polynomial is x²-√3x-√3..

➥VERIFICATION : -

★Sum of Zeroes : -

$\longmapsto\tt{\alpha+\beta=\dfrac{-b}{a}}$

$\longmapsto\tt{\sqrt{3}=\dfrac{-(-\sqrt{3)}}{1}}$

$\longmapsto\tt{\sqrt{3}=\sqrt{3}}$

$\green\longmapsto\tt\:\large\underline{\boxed{\bf\orange{L.H.S}\red{=}\blue{R.H.S}}}$

★ Product of Zeroes : -

$\longmapsto\tt{\alpha\beta=\dfrac{c}{a}}$

$\longmapsto\tt{-\sqrt{3}=-\sqrt{3}}$

$\orange\longmapsto\:\large\underline{\boxed{\bf\red{L.H.S}\green{=}\purple{R.H.S}}}$

Answer 2

Answer:

=x^2-√3.

Step-by-step explanation:

The zeroes is √3 and-√3.

Alpha (a)= √3, beta(b)=-√3.

We know that-

a+b=√3+(-√3).

=√3-√3=0.

a×b=√3×(-√3).

=-√3.

Then,

x^2-(a+b)x-(ab).

Putting the value of (a+b) and (ab) in the formula------

x^2-0x+(-√3).

x^2-√3. This is your answer.

Thank you.

And hit the brainlist.