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Dima020 [189]
2 years ago
5

Select the two values of x that are roots of this equation 3x^2 + 1 =5x

Mathematics
1 answer:
Zina [86]2 years ago
8 0

Answer:

x = 1.434 and x=0.232

Step-by-step explanation:

To find the root of the equation stated above we need to:

(1) Write the polynomial equation with zero on the right hand side:

3x^{2} + 1 = 5x ⇒ 3x^{2} -5x + 1 = 0

(2) Divide the whole equation by 3

3x^{2} -5x + 1 = 0 ⇒ x^{2} -\frac{5}{3}x + \frac{1}{3}= 0

(3) Use the quadratic formula to solve the quadratic equation:

The quadratic formula states that the two solutions for a quadratic equation is given by:

\frac{-b±\sqrt{b^{2} - 4ac}}{2a} (1)

In this case, a = 1, b = -\frac{5}{3}, c= \frac{1}{3}

Substituiting a, b and c in equation (1) We get:

\frac{-\frac{5}{3}±\sqrt{(-\frac{5}{3})^{2} - 4(1)(\frac{1}{3})}}{2(1)} (1)

The two solutions are:

x = 1.434 and x=0.232

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