The zeros of the polynomial px-3x2-1 are a 1-3 and 3 b 1-3 and -3 c -1-3 and -3 d 1-3 and -1-3

Let p(x)=3x^2 1 To find the zeroes of px, we have:p(x)=0 ⇒3x2 1=0 ⇒3x^2=1 ⇒x^2=1/3 ⇒ x=±1/√(3) ⇒x= 1/√(3) and x= 1/√(3) Hence, the correct option is (d). ...

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Standard IX

Mathematics

Zeroes of a Polynomial

The zeros of ...

Question

The zeros of the polynomial $p (x) = 3 x^{2} - 1$ are
(a) $\frac{1}{3}$ and 3
(b) $\frac{1}{\sqrt{3}}$ and $\sqrt{3}$
(c) $\frac{- 1}{\sqrt{3}}$ and $\sqrt{3}$
(d) $\frac{1}{\sqrt{3}}$ and $\frac{- 1}{\sqrt{3}}$

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Solution

Let $p (x) = 3 x^{2} - 1$
To find the zeroes of px, we have:p(x)=0

⇒ $3 x 2 - 1 = 0$

⇒ $3 x^{2} = 1$

⇒ $x^{2} = \frac{1}{3}$

⇒ $x = \pm \frac{1}{\sqrt{3}}$

⇒ $x = \frac{1}{\sqrt{3}}$ and $x = - \frac{1}{\sqrt{3}}$

Hence, the correct option is (d).

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Similar questions

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The zeros of the polynomial p(x)=3x2−1 are (a) 13 and 3 (b) 1√3 and √3 (c) −1√3 and √3 (d) 1√3 and −1√3

Let p(x)=3x2−1 To find the zeroes of px, we have:p(x)=0 ⇒3x2−1=0 ⇒3x2=1 ⇒x2=13 ⇒ x=±1√3 ⇒x=1√3 and x=−1√3 Hence, the correct option is (d).

The zeros of the polynomial $p (x) = 3 x^{2} - 1$ are
(a) $\frac{1}{3}$ and 3
(b) $\frac{1}{\sqrt{3}}$ and $\sqrt{3}$
(c) $\frac{- 1}{\sqrt{3}}$ and $\sqrt{3}$
(d) $\frac{1}{\sqrt{3}}$ and $\frac{- 1}{\sqrt{3}}$

Let $p (x) = 3 x^{2} - 1$
To find the zeroes of px, we have:p(x)=0

⇒ $3 x 2 - 1 = 0$

⇒ $3 x^{2} = 1$

⇒ $x^{2} = \frac{1}{3}$

⇒ $x = \pm \frac{1}{\sqrt{3}}$

⇒ $x = \frac{1}{\sqrt{3}}$ and $x = - \frac{1}{\sqrt{3}}$

Hence, the correct option is (d).