Solve Quadratic Equations in Excel: Step-by-Step with Physics-Based Case Study

📚 Real-Life Scenario: Ritu’s Physics Assignment

Ritu, a B.Sc. student in Delhi University, is working on a Physics assignment involving projectile motion. The equation for the height of a projectile is:

h(t) = -4.9t² + 19.6t + 1

She needs to find when the object hits the ground — that is, when h(t) = 0.

This leads to a quadratic equation, and she wants to solve it in Excel quickly using formulas instead of manual calculation.

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🧮 Standard Quadratic Equation Format

A quadratic equation is always of the form:

ax² + bx + c = 0

The formula to find the roots is:

x = [-b ± √(b² - 4ac)] / 2a

To find real roots, you must check the discriminant (D):

D = b² - 4ac

• If D > 0: Two distinct real roots
• If D = 0: One repeated real root
• If D < 0: No real roots (they are imaginary)

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✅ Step-by-Step: Identify Real Roots in Excel

Let’s say:

• a is in cell A1
• b is in cell B1
• c is in cell C1

For example:

• A1 = -4.9
• B1 = 19.6
• C1 = 1

Step 1: Calculate the Discriminant

In cell D1:

=B1^2 - 4*A1*C1

This gives the discriminant (D)

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Step 2: Check if Roots Are Real

In cell E1 (interpret the discriminant):

=IF(D1<0, "No Real Roots", IF(D1=0, "One Real Root", "Two Real Roots"))

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Step 3: Calculate the Real Roots (If Any)

If D1 is greater than or equal to 0:

Root 1:

=(-B1 + SQRT(D1)) / (2*A1)

Root 2:

=(-B1 - SQRT(D1)) / (2*A1)

Wrap these in an IF to avoid errors when roots are imaginary.

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📌 Application Example (Ritu’s Case)

With:

• a = -4.9
• b = 19.6
• c = 1

She enters these values into Excel and finds:

• Discriminant (D):
  19.6² - 4*(-4.9)*1 = 384.16 + 19.6 = 403.76
• Result:
  Two real roots exist.
• Root 1 ≈ 4.00 seconds (time when object hits the ground)
• Root 2 ≈ -0.05 seconds (not valid in real-world time)

📌 So Ritu uses only the positive root as her real-world answer.

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