The roots of the quadratic equation 3x^2 - 4x | vedclass

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Question

(D) To find the roots of the quadratic equation $3x^2 - 4x + 1 = 0$,we can use the splitting the middle term method.We need two numbers that multiply

Vedclass · Accepted Answer

$1, \frac{1}{3}$

Vedclass · Answer

(D) To find the roots of the quadratic equation $3x^2 - 4x + 1 = 0$,we can use the splitting the middle term method.We need two numbers that multiply to $(3 	imes 1) = 3$ and add to $-4$.These numbers are $-3$ and $-1$.Now,rewrite the equation: $3x^2 - 3x - x + 1 = 0$.Factor by grouping: $3x(x - 1) - 1(x - 1) = 0$.This gives $(3x - 1)(x - 1) = 0$.Setting each factor to zero:$3x - 1 = 0 \implies x = \frac{1}{3}$$x - 1 = 0 \implies x = 1$Therefore,the roots are $1, \frac{1}{3}$.

The roots of the quadratic equation $3x^2 - 4x + 1 = 0$ are:

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