Applying the Quadratic Formula with Decimal and Non-Integer Coefficients
Grade 9 students in California Reveal Math Algebra 1 learn to apply the Quadratic Formula to equations with decimal or fractional coefficients, using the same formula x=(-b±sqrt(b²-4ac))/(2a) but with extra care. The strategy is to compute b² and 4ac as separate steps to reduce decimal errors, carry extra decimal places throughout, and round only the final answer. For example, solving 1.2x²-4.5x+2.3=0 gives discriminant 9.21 and solutions x≈3.14 and x≈0.61. Always check whether both solutions make physical sense in context — a negative time solution should be discarded.
Key Concepts
The Quadratic Formula works for any quadratic equation $ax^2 + bx + c = 0$, including those with decimal or fractional coefficients. The same formula applies:.
$$x = \frac{ b \pm \sqrt{b^2 4ac}}{2a}$$.
Common Questions
Does the Quadratic Formula work with decimal coefficients?
Yes. The Quadratic Formula x=(-b±sqrt(b²-4ac))/(2a) works for any quadratic equation including those with decimal or fractional coefficients. The key is careful step-by-step arithmetic.
What strategy helps avoid errors with decimal coefficients?
Compute b² and 4ac as separate steps before subtracting to form the discriminant. Carry extra decimal places throughout and round only the final answer to the requested precision.
How do you solve 1.2x²-4.5x+2.3=0?
a=1.2, b=-4.5, c=2.3. Discriminant: (-4.5)²-4(1.2)(2.3)=20.25-11.04=9.21. Then x=(4.5±sqrt(9.21))/2.4=(4.5±3.035)/2.4, giving x≈3.14 or x≈0.61.
How do you solve 0.5x²+3x-1.75=0?
a=0.5, b=3, c=-1.75. Discriminant: 9-4(0.5)(-1.75)=9+3.5=12.5. Then x=(-3±sqrt(12.5))/1=(-3±3.536), giving x≈0.54 or x≈-6.54.
When should you reject one of the two solutions?
Reject solutions that are unreasonable in context. If x represents time in seconds, discard negative values. If x represents a count of items, discard non-integer or negative values.
Which unit covers the Quadratic Formula in Algebra 1?
This skill is from Unit 10: Quadratic Functions in California Reveal Math Algebra 1, Grade 9.