2023: Grade 11 Mathematics Investigation 2023
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Grade 11 Mathematics Investigation 2023 Questions and Answers Guide
Answers (For Guiding Purposes)
To solve the quadratic equation 2????^2 + 5???? − 2 = 0 using the quadratic formula, we need to first identify the values of a, b, and c in the general quadratic equation form, which is ax^2 + bx + c = 0.
In this case, a = 2, b = 5, and c = -2.
The quadratic formula is:
???? = (−???? ± √????^2 − 4????????) / 2????
Substituting the values of a, b, and c in the quadratic formula, we get:
???? = (−5 ± √5^2 − 4(2)(−2)) / 2(2)
Simplifying the equation further:
???? = (−5 ± √41) / 4
Therefore, the solutions to the quadratic equation 2????^2 + 5???? − 2 = 0 are ???? = (-5 + √41) / 4 or ???? = (-5 – √41) / 4. These roots are unequal because the discriminant (the expression inside the square root in the quadratic formula) is greater than zero.