Question

What are the roots of the quadratic equation 2x2+7x+4=0? Select all that apply.

A. −7+17√4
B. −7−17√4
C. −7+17√2
D.−7−17√2
E. 7+17√4
F. 7−17√4
G. 7+17√2
H. 7−17√2

Answer 1

option A and B

`x=\frac{-7+√(17)} {4}`

and

`x=\frac{-7-√(17)} {4}`

Explanation:

we have

`2x^2+7x+4=0`

The formula to solve a quadratic equation of the form

`ax^(2) +bx+c=0`

is equal to

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

in this problem we have

`2x^2+7x+4=0`

so

`a=2\\b=7\\c=4`

substitute in the formula

`x=\frac{-7\pm\sqrt{7^(2)-4(2)(4)}} {2(2)}`

`x=\frac{-7\pm√(17)} {4}`

so

`x=\frac{-7+√(17)} {4}`

and

`x=\frac{-7-√(17)} {4}`