The zeroes of the polynomial px-3 x2-1 area 13 and 3b 13 and 3c -13 and 3d 13 and-13

(d) 13 #160;and #160; 13 Let: px=3x2 1 To #160;find #160;the #160;zeroes #160;of #160;px, #160;we #160;have:px=0 #8658;3x2 1=0 nbsp; ...

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Standard IX

Mathematics

Zeroes of a Polynomial

The zeroes of...

Question

The zeroes of the polynomial p(x) = 3x² − 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

(d) $\frac{1}{\sqrt{3}} and \frac{- 1}{\sqrt{3}}$

Let:
$p (x) = 3 x^{2} - 1$

$To find the zeroes of p (x), we have : p (x) = 0 \Rightarrow 3 x^{2} - 1 = 0$
$\Rightarrow 3 x^{2} = 1 \Rightarrow x^{2} = \frac{1}{3} \Rightarrow x = \pm \frac{1}{\sqrt{3}} \Rightarrow x = \frac{1}{\sqrt{3}} and x = - \frac{1}{\sqrt{3}}$
Hence, the correct answer is option D.

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

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

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

The zeroes of the polynomial p(x) = 3x² − 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) $\frac{1}{\sqrt{3}} and \frac{- 1}{\sqrt{3}}$