Question

Can someone please help me with this; im a lil bit confused.... Q.solve for the values of x in the equation 2x² - 5x - 12 = 0 using the quadratic equation formula.​

Answer 1

The solutions for x are
`x = 4` and
`x = -1.5`.

Explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

`ax^(2) + bx + c, a\\eq0`.

This polynomial has roots
`x_(1), x_(2)` such that
`ax^(2) + bx + c = a(x - x_(1))*(x - x_(2))`, given by the following formulas:

`x_(1) = (-b + √(\Delta))/(2*a)`

`x_(2) = (-b - √(\Delta))/(2*a)`

`\Delta = b^(2) - 4ac`

2x² - 5x - 12 = 0

This means that
`a = 2, b = -5, c = -12`

Solution:

`\Delta = (-5)^2 - 4(2)(-12) = 121`

`x_(1) = (-(-5) + √(121))/(2*2) = 4`

`x_(2) = (-(-5) - √(121))/(2*2) = -1.5`

The solutions for x are
`x = 4` and
`x = -1.5`.