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If one root of the equation $3 x^{2} - 10 x + 3 = 0$ is $\frac{1}{3}$ then the other root is

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- \frac{1}{3}

3

- 3

\frac{1}{3}

answer is D.

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Detailed Solution

Given quadratic equation is,

3 x^{2} - 10 x + 3 = 0

.
One root of the equation is

\frac{1}{3}

.
Standard form of a quadratic equation is

a x^{2} + bx + c = 0,

where

a, b c

are real numbers and

a \neq 0

.
And, the sum of the roots is given by

- \frac{b}{a}

and product of the roots is given by

\frac{c}{a}

.
Comparing the equation

3 x^{2} - 10 x + 3 = 0

with the standard form, we get,

a = 3, b = - 10, c = 3

.
Let's consider m be another root of the equation then product of the roots is,

⟹ \frac{1}{3} \times m = \frac{3}{3}

⟹ \frac{m}{3} = 1

∴ m = 3

∴

If one root of the equation

3 x^{2} - 10 x + 3 = 0

\frac{1}{3}

then the other root is 3.
Hence, the correct option is 4.

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