Can a quadratic equation have three roots?

No. According to the Fundamental Theorem of Algebra, a polynomial equation of degree n has exactly n complex roots. A quadratic equation is a second-degree polynomial (n = 2) and thus can have at most two roots.

What are imaginary roots?

When the discriminant D = b² - 4ac is negative, the square root term contains a negative value, yielding roots with the imaginary unit i (where i = √-1). These are complex numbers representing points where the parabola does not cross the x-axis.

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Class IX Mathematics

Chapter 8: Quadrilaterals

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Worksheet Details:

• Title: Class IX Math: Quadrilaterals Printable Sheet
• Format: Print Optimized CSS stylesheet
• Sections: Formulas checklist, 5 assessment questions, worked keys

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Class IX Mathematics: Quadrilaterals

Name: ______________________Date: __________________Score: ______ / 5

Section I: Key Formulas

Mid point Theorem

DE = \frac{1}{2}BC \land DE \parallel BC

Section II: Answer the Questions

1. A dome of a building is in the form of a hemisphere. From inside, it was white -washed at the cost of Rs 498.96. If the cost of white-washing is Rs 2.00 per square metre, find the (i) inside surface area of the dome, (ii) volume of the air inside the dome.

Solve and write the step-by-step solution in the workspace below.

2. How many square metres of canvas is required for a conical tent whose height is 3.5 m and the radius of whose base is 12 m?

Solve and write the step-by-step solution in the workspace below.

3. [Worksheet Question 1] Apply the formula Mid point Theorem to solve for coefficient constants. What is the value?

[ ] A. Constant value[ ] B. Dependent variable[ ] C. Zero[ ] D. Undefined

4. [Worksheet Question 2] Apply the formula Mid point Theorem to solve for coefficient constants. What is the value?

[ ] A. Constant value[ ] B. Dependent variable[ ] C. Zero[ ] D. Undefined

5. [Worksheet Question 3] Apply the formula Mid point Theorem to solve for coefficient constants. What is the value?

[ ] A. Constant value[ ] B. Dependent variable[ ] C. Zero[ ] D. Undefined

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