Helppp with this math question!?

Question

Select the approximate values of X that are solutions to f(x)=0, where f(x)=-2x^2+6x+7. 



A. {-0.29,0.86} 

B. {-2,6} 

C. {-3.00,-3.50} 

D. {-0.90, 3.90}

 

 

Answer 1

The function is f (x) = - 2x² + 6x + 7 = 0.

- 2x² + 6x + 7 = 0, is a quadratic, use quadratic formula to find the roots of the related quadratic equation.

Solution of the quadratic equation : x = [- b ± √(b² - 4ac)]/2a.

Compare the given equation with standard form of the quadratic equation ax² + bx + c = 0.

a = - 2, b = 6 and c = 7.

Solution : x = [- 6 ± √(6² - (4*(- 2)*(7)))]/2*(- 2)

= [- 6 ± √(36 + 56)]/(- 4)

= [- 6 ± √92]/(- 4)

= [6 ± 2√23]/4

= [3 ± √23]/2

⇒x = (3 - √23)/2 and x = (3 + √23)/2

x = - 0.8979 and x = 3.8979.

The solutions are x = - 0.90 and x = 3.90(approximate values of x).

 

Option D is the correct choice.