Quadratic Equations

Concept: Use the quadratic formula:

x%20%3D%20%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D

for equation

ax%5E2%20%2B%20bx%20%2B%20c%20%3D%200

.
Step 1: Identify coefficients. Given:

x%5E2%20-%205x%20-%2010%20%3D%200

a%20%3D%201%2C%5Cquad%20b%20%3D%20-5%2C%5Cquad%20c%20%3D%20-10

Step 2: Substitute into formula.

x%20%3D%20%5Cfrac%7B-(-5)%20%5Cpm%20%5Csqrt%7B(-5)%5E2%20-%204(1)(-10)%7D%7D%7B2(1)%7D

x%20%3D%20%5Cfrac%7B5%20%5Cpm%20%5Csqrt%7B25%20%2B%2040%7D%7D%7B2%7D

Step 3: Simplify.

x%20%3D%20%5Cfrac%7B5%20%5Cpm%20%5Csqrt%7B65%7D%7D%7B2%7D

Step 4: Approximate value.

%5Csqrt%7B65%7D%20%5Capprox%208.062

x_1%20%3D%20%5Cfrac%7B5%20%2B%208.062%7D%7B2%7D%20%3D%20%5Cfrac%7B13.062%7D%7B2%7D%20%5Capprox%206.53

x_2%20%3D%20%5Cfrac%7B5%20-%208.062%7D%7B2%7D%20%3D%20%5Cfrac%7B-3.062%7D%7B2%7D%20%5Capprox%20-1.53

Conclusion: The solutions correct to two decimal places are:

x%20%3D%206.53%20%5Cquad%20%5Ctext%7Bor%7D%20%5Cquad%20x%20%3D%20-1.53

Chapter Questions
1 MCQs