Final answer:
The zeros of the quadratic function y = x² - 13x + 12 are found using the quadratic formula. Substituting a = 1, b = -13, and c = 12 into the formula yields two solutions: x = 12 and x = 1.
Step-by-step explanation:
The question asks to find all the zeros of the quadratic function y = x² - 13x + 12. To solve for the zeros of a quadratic function, which is of the form ax² + bx + c = 0, we can use the quadratic formula. For the given function, we can identify a = 1, b = -13, and c = 12, and substitute these values into the quadratic formula: x = –b ± √(b² - 4ac) / (2a).
Therefore, the zeros are found by calculating:
x = –(-13) ± √((-13)² - 4(1)(12)) / (2(1))
= 13 ± √(169 - 48) / 2
= 13 ± √(121) / 2
= 13 ± 11 / 2
Which gives us two solutions for x:
x = (13 + 11) / 2 = 12
x = (13 - 11) / 2 = 1
Therefore, the zeros of the function y = x² - 13x + 12 are x = 12 and x = 1.