The roots of the quadratic equation 3 x 2-2 x -1-0 areA- -1- B- -2- 1-3C- 1- 1-3D- 2-3

The correct option is A 1, 1/33x^2+2x 1 = 0 ⇒ 3x^2+3x x 1 = 0 ⇒ 3x (x+1) 1 (x+1) nbsp;= 0 ⇒ (3x 1) (x+1) = 0 ⇒ (3x 1)=0 or (x+1)=0 ⇒ x = 1/3 or x= 1 ∴ The ...

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Byju's Answer

Standard IX

Mathematics

Sum and Product of Roots of a Quadratic Equation

The roots of ...

Question

The roots of the quadratic equation $3 x^{2} + 2 x - 1 = 0$ are .

-1,

\frac{1}{3}

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-2,

\frac{1}{3}

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\frac{1}{3}

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2, 3

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Solution

The correct option is A -1, $\frac{1}{3}$
$3 x^{2} + 2 x - 1 = 0$
$\Rightarrow 3 x^{2} + 3 x - x - 1 = 0$
$\Rightarrow 3 x (x + 1) - 1 (x + 1) = 0$
$\Rightarrow (3 x - 1) (x + 1) = 0$
$\Rightarrow$ $(3 x - 1) = 0 o r (x + 1) = 0$
$\Rightarrow x = \frac{1}{3} o r x = - 1$
$∴$ The roots of the given equation are $- 1$ , $\frac{1}{3}$ .

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The roots of the quadratic equation 3x2+2x−1=0 are .

The correct option is A -1, 133x2+2x−1=0 ⇒3x2+3x−x−1=0 ⇒3x(x+1)−1(x+1)=0 ⇒(3x−1)(x+1)=0 ⇒ (3x−1)=0 or (x+1)=0 ⇒x=13 or x=−1 ∴ The roots of the given equation are −1, 13 .

The roots of the quadratic equation $3 x^{2} + 2 x - 1 = 0$ are .