Question

The quadratic formula is used to solve for ???? in equations taking the form of a quadratic equation, ????????2+????????+????=0. quadratic formula:????=−????±√(????^2−4????????)/2????. Solve for ???? in the expression using the quadratic formula. 2????^2+31????−6.1=0. Use at least three significant figures in each answer.

Answer 1

Using the quadratic formula

`x=\frac{-b+/-\sqrt{b^(2)-4ac } }{2a}`

The answer to the equation
`2x^(2) +31x-6.1=0` using at least three significant figures is:

`x_(1)=0.194\\x_(2)=-15.694`

Explanation:

The quadratic formula is used to solve polynomials of second degree.

We have a polynomial of second degree to be resolved with the quadratic formula:

`2x^(2) +31x-6.1=0` (Eq. 1)

We know the quadratic formula is:

`x=\frac{-b+/-\sqrt{b^(2)-4ac } }{2a}` (Eq. 2)

To resolve the quadratic formula we need the a, b and c coefficients, we can find these coefficients in the equation 1.

a: Coefficient that accompanies
`x^(2)`

b: Coefficient that accompanies
`x`

c: Independent term

With this information and the equation (1). We know the values of a, b and c

`a=2\\b=31\\c=-6.1\\`

Now, we can replace these terms in the quadratic formula (Eq. 2)

The first root will be found using the positive sign before the square root:

`x=\frac{-b+\sqrt{b^(2)-4ac } }{2a}`

`x=\frac{-31+\sqrt{31^(2)-[4*2*(-6.1)]} }{2*2}`

`x=(-31+√(961-(-48.8)) )/(4)`

`x=(-31+√(961+48.8) )/(4)`

`x=(-31+√(1009.8) )/(4)`

`x=(-31+31.777 )/(4)`

`x=0.194`

The second root will be found using the negative sign before the square root

:

`x=\frac{-b-\sqrt{b^(2)-4ac } }{2a}`

`x=\frac{-31-\sqrt{31^(2)-[4*2*(-6.1)]} }{2*2}`

`x=(-31-√(961-(-48.8)) )/(4)`

`x=(-31-√(961+48.8) )/(4)`

`x=(-31-√(1009.8) )/(4)`

`x=(-31-31.777 )/(4)`

`x=-15.694`