Value of x

Question

Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -7x2 + 5x + 5.

{1.27, –0.56}

{-7, 5}

{–0.71, –0.71}

{–1.40, 1.00}

Answer 1

For this one, you pop the values of the coefficients into the quadratic equation.  This is a second order equation, so there are at most two correct answers.

 

(-b +/- sqrt(b^2 - 4ac)) / 2a

 

so, from the inside -

b^2-4ac = 5*5-4*(-7)*5 = 25 +140 = 165

 

sqrt(165) = 12.84

 

Now drop that value in for the entire sqrt term, and drop in the other coefficients, and we get

 

(-5 +/- 12.84)/(2*-7)

 

which comes out to -0.56 and 1.27, the first answers.