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Quadratic Formula

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1 Answer

0 = -6 x^2 + 7 x + 8
 
x = (-7 ± sqrt(7^2 - 4(-6)(8)))/(2(-6))
 
x = 7/12 ± sqrt(1 + 48 + 4(48))/12
 
x = 7/12 ± sqrt(1 + 48 (1 + 4))/12
 
x = 7/12 ± sqrt(1 + 48 (10/2))/12
 
x = 7/12 ± sqrt(241)/12
 
x = 0.58333333333333 ± 1.29368122468834
 
x = 1.88 or -0.71 => answer is A

Comments

This really helped me a lot. Thank you Steve so much!!!! I am practicing with a classmate to prepare for our college algebra final in two weeks and we have practice problems we can practice with but if we both come up with a different answer, we need help understanding where we went wrong, such as missing a step. We really liked the way you showed how you got this answer, this really helps!!! We do not have a answer sheet for these practice problems so we can not check the answers. We are very grateful.
You can check your answers. Just plug them back into the function for x and solve; if they're right you'll get zero for the function value (or close to it if you have some roundoff error).
 
You can use Synthetic Substitution and the Remainder Theorem; e.g., to check x = 1.88:
 
1.88 | -6    7          8
             -11.28  -8.0464
         ----------------------
         -6  -4.28 | -0.0464 ≈ 0 because we have some roundoff errors.
                       ----------- 
 
Note: I'm sure the structure above will not come out correctly; see your text's examples of using Synthetic Division / Substitution.