Question

Solve the quadratic equation 2x²−17x−1 using the quadratic formula.

a) x= 17+√297/4
b) x= 17−√297/4
c) x=17+√289/4
d) x=17− √289/4
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Answer 1

The quadratic equation 2x² - 17x - 1 can be solved using the quadratic formula, yielding two solutions: x = (17 + √297) / 4 and x = (17 - √297) / 4.

Step-by-step explanation:

To solve the quadratic equation 2x² - 17x - 1 using the quadratic formula, we'll plug our coefficients (a=2, b=-17, c=-1) into the formula:

x = (-b ± √b² - 4ac) / (2a)

Which gives us:

x = (17 ± √((-17)² - 4 · 2 · (-1))) / (2 · 2)

x = (17 ± √(289 + 8)) / 4

x = (17 ± √297) / 4

So, the solutions are:

x = (17 + √297) / 4

x = (17 - √297) / 4

While the student's options are similar, none match the correct calculation exactly, due to incorrect square root values or missing the division by 4.