Question

If (√3) and (– √3) are two zeroes of a quadratic polynomial, then the Polynomial is :-​

Answer 1

Given :

Given that $\sqrt{3}$ and $-\sqrt{3}$ are two zeroes of a polynomial.

To find :

Here, we have to find the polynomial having the zeroes mentioned above.

Solution :

Let :

• $\sqrt{3}$ be α.
• $-\sqrt{3}$ be β.

Now :

• Sum of the zeroes = α + β
• $\sqrt{3}+(-\sqrt{3})$
• $\sqrt{3}-\sqrt{3}$
• $0$

Also :

• Product of the zeroes = αβ
• $\sqrt{3}(-\sqrt{3})$
• $-3$

We know that :

• Polynomial : $x^2-(\alpha+\beta)x+(\alpha\beta)$

Now, substituting the values :

• $x^2-(0)x+(-4)$
• $x^2 - 4$

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☆ Therefore, the required polynomial is x² - 4.