One root of the equation 3x^2 - 10x + 3 = 0 i | vedclass

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Question

(A) The given quadratic equation is $3x^2 - 10x + 3 = 0$.Comparing this with the standard form $ax^2 + bx + c = 0$,we get $a = 3$,$b = -10$,and $c = 3

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(A) The given quadratic equation is $3x^2 - 10x + 3 = 0$.Comparing this with the standard form $ax^2 + bx + c = 0$,we get $a = 3$,$b = -10$,and $c = 3$.According to the properties of quadratic equations,the sum of the roots is given by $-\frac{b}{a}$.Sum of the roots $= -\frac{-10}{3} = \frac{10}{3}$.Let the roots be $\alpha$ and $\beta$. We are given $\alpha = \frac{1}{3}$.Since $\alpha + \beta = \frac{10}{3}$,we have $\frac{1}{3} + \beta = \frac{10}{3}$.Therefore,$\beta = \frac{10}{3} - \frac{1}{3} = \frac{9}{3} = 3$.The other root is $3$.

One root of the equation $3x^2 - 10x + 3 = 0$ is $\frac{1}{3}$. Find the other root.

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