Solve using the quadratic formula.5y2−8y+2=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.y=_____ or y=_____
Q. Solve using the quadratic formula.5y2−8y+2=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.y=_____ or y=_____
Identify values: Identify the values of a, b, and c in the quadratic equation5y2−8y+2=0. The quadratic equation is in the form ay2+by+c=0. For our equation, a=5, b=−8, and c=2.
Substitute in formula: Substitute the values of a, b, and c into the quadratic formula y=2a−b±b2−4ac. Substitute a=5, b=−8, and c=2 into the formula. y=2⋅5−(−8)±(−8)2−4⋅5⋅2y=108±64−40
Simplify and calculate discriminant: Simplify the expression under the square root and calculate the discriminant. 64−40=24 The discriminant is 24, which is positive, indicating that we will have two real solutions.
Continue simplifying formula: Continue simplifying the quadratic formula with the calculated discriminant.y=108±24y=108±26y=54±6
Write possible solutions: Write the two possible solutions for y.y=54+6 or y=54−6
Round if necessary: If necessary, round the values of y to the nearest hundredth.y≈(4+2.45)/5 or y≈(4−2.45)/5y≈6.45/5 or y≈1.55/5y≈1.29 or y≈0.31
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