Solve using the quadratic formula.4m2−m−9=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.m=_____ or m=_____
Q. Solve using the quadratic formula.4m2−m−9=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.m=_____ or m=_____
Quadratic Formula Definition: The quadratic formula is given by m=2a−b±b2−4ac, where a, b, and c are the coefficients of the terms in the quadratic equationax2+bx+c=0. In this case, a=4, b=−1, and c=−9.
Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4ac. Here, b2=(−1)2=1 and 4ac=4×4×(−9)=−144. So, the discriminant is 1−(−144)=1+144=145.
Plug Values into Formula: Now, plug the values of a, b, and the discriminant into the quadratic formula to find the two possible values for m. This gives us m=2×4−(−1)±145.
Simplify Equation: Simplify the equation by calculating the numerator for both the plus and minus scenarios. For the plus scenario: m=81+145. For the minus scenario: m=81−145.
Calculate Decimal Values: Since the discriminant is a non-perfect square, the square root of 145 cannot be simplified to a rational number. Therefore, we will leave the square root as is and express m as two decimals rounded to the nearest hundredth. Calculate the decimal values: m≈(1+12.04)/8 and m≈(1−12.04)/8.
Perform Calculations: Perform the calculations for both scenarios. For the plus scenario: m≈(1+12.04)/8≈13.04/8≈1.63. For the minus scenario: m≈(1−12.04)/8≈−11.04/8≈−1.38.
More problems from Solve a quadratic equation using the quadratic formula