Question

How do you solve `4x^2-13x+3=0`?

Answer 1

`x=1/4, 3`

Explanation:

`4x^2-13x+3=0` is a quadratic equation with the form `ax^2+bx+c=0`, where `a=4,` `b=-13,` and `c=3`.

Use the quadratic formula.

`x=(-b+-sqrt(b^2-4ac))/(2a)`

`x=(-(-13)+-sqrt(-13^2-4*4*3))/(2*4)` =

`x=(13+-sqrt(169-48))/8` =

`x=(13+-sqrt(121))/8` =

`x=(13+-11)/8`

Solve for `x`.

`x=(13+11)/8=24/8=3`

`x=(13-11)/8=2/8=1/4`

Answer 2

Solve: y = 4x^2 - 13x + 3 = 0
Answers: 1/4 and 3

Explanation:

Use the new Transforming Method (Google and Yahoo Search)
Transformed equation: y' = x^2 - 13x + 12. Both roots are positive.
Factor pairs of ac = 12 --> (1, 12) = 13.
y1 = 1 and y2 = 12
x1 = y1/a = 1/4 and x2 = y2/a = 12/4 = 3
Answers: 1/4 and 3.

Note : I advise students to learn and solve quadratic equations by the new Transforming Method. It is simpler and faster than using the formula or the factoring by grouping method.