What is the solution to the quadratic equation 2x^2 - 5x + 3 = 0?

Question

In this question, we are given a quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are coefficients. The task is to find the values of x that satisfy the equation. To solve this quadratic equation, we can use various methods such as factoring, completing the square, or applying the quadratic formula.

Answer: You can find the solution to the quadratic equation 2x^2 - 5x + 3 = 0 on the website: helpinhomework.org

Answer 1

2x^2 -5x+3 =0

factor

(2x-3)(x-1)=0

x-1=0, 2x-3=0

x =1 or 3/2

use the quadratic formula

x=5/4 +/-(1/4)sqr(25-4(2)(3))

= (5+/-1)/4 = 6/4, 4/4

= 1.5, or 1

complete the square

2(x^2-5x/2) + 3 =0

2(x^2-5x/2 +25/16) = -3 + (25/16)2

2(x-5/4)^2 = (50-48)/16

(x-5/4)^2 = 1/16

x-5/4 = +/-1/4

x = 5/4 +/-14

x = 6/4. 4/4

x = 3/2, 1

or use a graphing calculator

and see where the graph intersects

the x axis

the equation solutions are the same

as the x intercepts, zeros or roots

or use an online equation calculator

it's often useful to solve the problem with more than one method to check your answers

if you get 2 different answers, at least one of them is wrong

y=2x^2-5x +3 is an upward opening parabola since the x^2 coefficient >0

y'(x) = 4x-5=0, x=5/4 = x coordinate of the vertex = minimum point

y coordinate of the vertex = 2(5/4)^2-5(5/4)+3 = -1/16

in vertex form it's

2(x -5/4)^2 -1/16, vertex=(5/4, -1/16) = minimum point

the x coordinate also is the axis of symmetry, x=5/4 = 1.25

the x intercepts are equidistant to the axis of symmetry, 5/4-1 = 3/2-5/4 = 1/4

using descartes rule, you know there is a maximum 2 positive solutions

as the sign changes twice from 2x^2 to -5x to +3

replace x with -x to see the maximum number of negative solutions

2(-x)^2 -5(-x) +3 has no sign changes, therefore there are zero negative solutions

either there are 2 positive real solutions or there are 2 imaginary solutions

for this specific example, there are 2 real positive and 0 negative and 0 imaginary solutions