Solve a) 2x² + x − 4 = 0 and b) x² + x = 0

An equation of the form of ax² + bx + c = 0 is called a quadratic equation.

Answer: a) 2 x² + x − 4 = 0  is x = - 1 - √33 / 4, - 1 + √33 / 4 and b) x² + x = 0 is x = 0,- 1. 

Let's find the values of x.

Explanation:

We know that the standard form of a quadratic equation is given by,

ax² + bx + c = 0

We can solve the above quadratic equations using quadratic formula ⇒ x = -b ± √ (b² - 4ac) / 2a.

Discriminant = b² - 4ac

a) 2x² + x − 4 = 0

Here a = 2, b = 1 and c = -4

⇒ x = -1 ± √ 1² - 4(2)(-4) / 2(2)

⇒ x = -1 ± √ (1 + 32) / 4

⇒ x = -1 ± √ 33 / 4

⇒ x = -1 - √ 33 / 4 or  -1 + √ 33 / 4

b) x² + x = 0

Here, a = 1, b = 1 and c = 0

⇒ x = -1 ± √ 1² - 4(1)(0) / 2(1)

⇒ x = -1 ± √ (1 - 0) / 2

⇒ x = -1 ± √ 1 / 2 

⇒ x = (-1 ± 1) / 2

⇒ x = (-1 + 1) / 2 or (-1 - 1) / 2 

⇒ x = 0 / 2 or -2 / 2

⇒ x = 0  or -1

We can use cuemath's online quadratic equation calculator to solve the equations for the values of 'x'.

Thus, the solution for a) 2x² + x − 4 = 0  is x = -1 - √ 33 / 4 or  -1 + √ 33 / 4 and b) x² + x = 0 is x = 0  or -1.