Find out 3p²-8p+4

Answer 1

To solve the quadratic expression ( 3p^2 - 8p + 4 ), you can use different methods depending on what is required:

1. **Factorization**: Check if the expression can be factored into simpler expressions. For ( 3p^2 - 8p + 4 ), you look for two numbers that multiply to ( 3 \cdot 4 = 12 ) (coefficient of ( p^2 ) times constant term) and add up to ( -8 ) (coefficient of ( p )). The factors of ( 3 \cdot 4 = 12 ) that add up to ( -8 ) are ( -6 ) and ( -2 ). So, you can factor it as:

   [ 3p^2 - 8p + 4 = (3p - 2)(p - 2) ]

   This is the factored form of the quadratic expression.

2. *Quadratic Formula*: If factoring is not possible or preferred, you can use the quadratic formula ( p = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ), where ( a = 3 ), ( b = -8 ), and ( c = 4 ) (from ( 3p^2 - 8p + 4 = 0 )). Calculate as follows:

   [ p = \frac{-(-8) \pm \sqrt{(-8)^2 - 4 \cdot 3 \cdot 4}}{2 \cdot 3} ] [ p = \frac{8 \pm \sqrt{64 - 48}}{6} ] [ p = \frac{8 \pm \sqrt{16}}{6} ] [ p = \frac{8 \pm 4}{6} ]

   This gives two solutions: [ p_1 = \frac{8 + 4}{6} = \frac{12}{6} = 2 ] [ p_2 = \frac{8 - 4}{6} = \frac{4}{6} = \frac{2}{3} ]

   So, the solutions to ( 3p^2 - 8p + 4 = 0 ) are ( p = 2 ) and ( p = \frac{2}{3} ).

3. *Completing the Square*: Another method involves completing the square, which transforms the quadratic into a perfect square trinomial. This method is less commonly used but can be applied if necessary.

These methods provide different approaches to solving ( 3p^2 - 8p + 4 ), depending on whether you need to factorize it, find exact solutions, or explore the quadratic formula for roots.