Question

Use the quadratic formula to find the exact solutions of x2 − 5x − 2 = 0.

Answer 1

`x=(5 \pm √(33))/(2)`

Explanation:

Quadratic Formula

`x=(-b \pm √(b^2-4ac) )/(2a)\quad\textsf{when }\:ax^2+bx+c=0`

Given equation:

`x^2-5x-2=0`

Comparing the given equation with
`ax^2+bx+c=0` to find the values of a, b and c:

• a = 1
• b = -5
• c = -2

Substitute these values into the quadratic formula and solve for x:

`\implies x=(-(-5) \pm √((-5)^2-4(1)(-2)))/(2(1))`

`\implies x=(5 \pm √(25+8))/(2)`

`\implies x=(5 \pm √(33))/(2)`

Answer 2

Solutions given:

given equation is

x²-5x-2=0

comparing above equation with ax²+bx+c,we get

a=1

b=-5

c=-2

By using quadratic equation

x=
`\frac{ - b± \sqrt{ {b}^(2) - 4ac} }{2a}`

x=
`\frac{ 5± \sqrt{ {-5}^(2) - 4*1*-2}}{2*1}`

x=
`( 5± √( 25+8))/(2*1)`

x=
`( 5± √( 33 ))/(2)` is a required answer.