Question

Solve the equation 3x^2-2x-10=0

Show all your working and give your answers correct to 2 decimal place

Answer 1

Explanation:

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 3

B = -2

C = -10

B2 - 4AC =

4 - (-120) =

= 124

Applying the quadratic formula :

2 ± √ 124

x = —————

6

√ 124 simplified

The prime factorization of 124 is

2•2•31

To be able to remove something from under the radical, there have to be 2 instances of it

√ 124 = √ 2•2•31 =

± 2 • √ 31

√ 31, rounded to 4 decimal digits, is 5.5678

So now we are looking at:

x = ( 2 ± 2 • 5.568 ) / 6

Two real solutions:

x =(2+√124)/6=(1+√ 31 )/3= 2.189

or:

x =(2-√124)/6=(1-√ 31 )/3= -1.523

Answer 2

Explanation:

3x^2-2x-10=0

This is a quadratic equation that can be solved using the quadratic formula where

a = 3, b = -2, and c = -10

x=−b±(b^2−4ac)^(1/2)/2a

x=−(−2)±((−2)2−4(3)(−10)^(1/2)/2(3))

x=2±(124)^(1/2)/6

Simplify the Radical:

x=((2/6) ±2(31)^(1/2))/6

x=26±231−−√6

Simplify fractions and/or signs:

x=1/3±√31/3

which becomes

x=2.18925

See the attached image for a more clear display of solving using the quadratic equation.

x=−1.52259