Question

What are the approximate solutions of 2x2 + 9x = 8 to the nearest hundredth?

a. x ≈ 1.22 and x ≈ 3.28
b. x ≈ −0.76 and x ≈ 5.26
c. x ≈ −1.22 and x ≈ −3.28
d. x ≈ −5.26 and x ≈ 0.76

Answer 1

the anwser is d, hope this helps

Answer 2

The roots of the equations are x ≈ -5.26 and x ≈ 0.76 .

Option (d) is correct.

Explanation:

Formula for the roots is given by .

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

As the equation in the form

`2x^(2) + 9x - 8 = 0`

As the equation in the form ax² + bx + c = 0

a = 2, b= 9 , c = -8

Put in the formula

`x = \frac{-9 \pm \sqrt{9^(2) -4* 2* -8}}{2* 2}`

`x = (-9 \pm √(81 + 64))/(4)`

`x = (-9 \pm √(145))/(4)`

`√(145) = 12.04`

Thus First roots be

`x = (-9 - 12.04)/(4)`

`x = (-21.04)/(4)`

x ≈ -5.26

The second root be

`x = (-9 + 12.04)/(4)`

`x = (3.04)/(4)`

x ≈ 0.76

Therefore the roots of the equations are x ≈ -5.26 and x ≈ 0.76 .

Option (d) is correct.