Question

find the roots of the equation 2x 2 – 5x + 3 = 0, by using quadratic formula.

Answer 1

formula method x=3/2 and x=1

Answer 2

Given,

A quadratic equation: 2x^2 – 5x + 3 = 0

To find,

The roots of the given equation by using the quadratic formula.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

If ax^2 + bx + c = 0 is a quadratic equation, then, it's both roots X1 and X2 can be calculated by using the quadratic formula method, as follows:

X1 = {-b + √(b^2-4ac)}/2a

X2 = {-b - √(b^2-4ac)}/2a

Now, according to the question;

For the given quadratic equation,

a = 2

b = -5

c = 3

Now, both roots of the given quadratic equation, X1 and X2 can be calculated by using the quadratic formula method, as follows:

X1 = {-b + √(b^2-4ac)}/2a

= {-(-5) + √((-5)^2-4(2)(3))}/2(2)

= {5 + √(25-24)}/4

= {5 + √(1)}/4

= 6/4 = 1.5

X2 = {-b - √(b^2-4ac)}/2a

= {-(-5) - √((-5)^2-4(2)(3))}/2(2)

= {5 - √(25-24)}/4

= {5 - √(1)}/4

= 6

= 4/4 = 1

Hence, both roots of the given quadratic equation are 1 and 1.5, respectively.