Solve using the quadratic formula.5p2−3p−8=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.p=_____ or p=_____
Q. Solve using the quadratic formula.5p2−3p−8=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.p=_____ or p=_____
Identify Coefficients: Identify the coefficients of the quadratic equation.The quadratic equation is in the form ap2+bp+c=0. For the equation 5p2−3p−8=0, the coefficients are:a = 5b = −3c = −8
Substitute into Formula: Substitute the coefficients into the quadratic formula.The quadratic formula is p=2a−b±b2−4ac. Substituting the values we get:p=2⋅5−(−3)±(−3)2−4⋅5⋅(−8)p=103±9+160
Simplify Square Root: Simplify under the square root.Calculate the value inside the square root: 9+160=169
Simplify Root: Simplify the square root.Since 169 is a perfect square, we find that:169=13
Calculate Solutions: Calculate the two possible solutions for p.Now we have two possible solutions for p:p=103+13 or p=103−13p=1016 or p=10−10
Simplify Fractions: Simplify the fractions.Simplify the fractions to get the solutions in simplest form:p=58 or p=−1
Convert to Decimal: Convert to decimal if necessary.If we need the solutions as decimals rounded to the nearest hundredth:p≈1.60 or p=−1.00
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