Question

find the roots of the equation 3x²-5x+2=0 by quadratic formula

Answer 1

Answer:

Step-by-step explanation:

3x²-5x+2=0

3x²-3x-2x+2=0

3x(x-1)-2(x-1)=0

(X-1)(3x-2)=0

X-1=0

X=1

3x-2=0

3x=2

X=2/3

Answer 2

The roots of the equation 3x²-5x+2=0 by quadratic formula are x = 1 and x = 2/3.

Given,

The quadratic equation 3x²-5x+2=0

To Find,

The roots of the given quadratic equation

Solution,

Quadratic equations are a form of polynomial equations with degree 2 in one variable. It can be expressed in the form f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0

In the given quadratic equation,

a = 3

b = -5

c = 2

The solution for quadratic equation could be found out using the quadratic formula, which is given as follows:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Substituting the values in the given formula, we get

$\implies x = \frac{5 \pm \sqrt{5^2 - 4\times3\times2}}{2\times3}\\\\\implies x = \frac{5 \pm \sqrt{25 - 24}}{6}\\\\\implies x = \frac{5 \pm \sqrt{1}}{6}\\\\\implies x = \frac{5 \pm 1}{6}\\\\\implies x = \frac{5+1}{6} \hspace{0.2 cm} or \hspace{0.2 cm} x = \frac{5-1}{6}\\\\\implies x = \frac{6}{6} \hspace{0.2 cm} or \hspace{0.2 cm} x = \frac{4}{6}\\\\\implies x = 1 \hspace{0.2 cm} or \hspace{0.2 cm} x = \frac{2}{3}$

Therefore, the roots of the equation 3x²-5x+2=0 by quadratic formula are x = 1 and x = 2/3.

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