Solve using the quadratic formula.u2+5u−3=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.u=_____ or u=_____
Q. Solve using the quadratic formula.u2+5u−3=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.u=_____ or u=_____
Quadratic Formula: The quadratic formula is given by u=2a−b±b2−4ac, where a, b, and c are the coefficients from the quadratic equationau2+bu+c=0. In our case, a=1, b=5, and c=−3.
Calculate Discriminant: First, we calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4ac. So we have 52−4(1)(−3)=25+12=37.
Apply Quadratic Formula: Now we can apply the quadratic formula with our values for a, b, and c. We have u=2×1−5±37.
Calculate Solutions: We will have two solutions, one for the addition and one for the subtraction. Let's calculate them separately.For the addition: u=2−5+37.For the subtraction: u=2−5−37.
Express Solutions as Decimals: The solutions are not integers or proper fractions, and we cannot simplify 37 any further. So we will express the solutions as decimals rounded to the nearest hundredth.For the addition: u≈(−5+6.08)/2≈1.08/2≈0.54.For the subtraction: u≈(−5−6.08)/2≈−11.08/2≈−5.54.
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