Question

Select the two values of x that are roots of this equation.
3x2 + 1 = 5x

Answer 1

Answer:

x=(5+sqrt(13))/6, (5-sqrt(13))/6.

Step-by-step explanation:

3x^2+1=5x

3x^2-5x+1=0

Apply the quadratic formula with a=3, b=-5 and c=1.

Answer 2

The roots of the quadratic equation $3x^{2} +1-5x=0$ are $x=\frac{5\±\sqrt{13} }{6}$

The two values of x are the roots of the given equation.

Solution:As we know the Sidharacharya method for finding the roots of the quadratic equation.

options B and C are the correct roots of the given quadratic equation.

We will apply here that method.

So, that formula is

$x=\frac{-b\±\sqrt{b^{2}-4ac } }{2a}$

Here, b=-5, a=3 and c=1 comparing the given quadratic equation with ax^2+bx+c=0

Therefore, $x=\frac{-(-5)\±\sqrt{(5)^{2}-4*3*1 } }{2*3}$

         ⇒    $x=\frac{5\±\sqrt{25-12 } }{6}$

         ⇒    $x=\frac{5\±\sqrt{13 } }{6}$

Hence, the two values of x of given quadratic equations are $x=\frac{5+\sqrt{13 } }{6}$ and $x=\frac{5-\sqrt{13 } }{6}$

Therefore, options b and c are the correct roots of the given quadratic equation.

What is a Quadratic equations?

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).

What are the 3 types of quadratic equations?

There are three commonly-used forms of quadratics:

Standard Form: y = a x 2 + b x + c y=ax^2+bx+c y=ax2+bx+c.

Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y=a(x-r_1)(x-r_2) y=a(x−r1)(x−r2)

Vertex Form: y = a ( x − h ) 2 + k y=a(x-h)^2+k y=a(x−h)2+k.

Learn more about quadratic equations, refer to:

https://brainly.com/question/1214333

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