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 4: Linear Equations in Two Variables

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Worksheet Details:

• Title: Class IX Math: Linear Equations in Two Variables Printable Sheet
• Format: Print Optimized CSS stylesheet
• Sections: Formulas checklist, 5 assessment questions, worked keys

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Class IX Mathematics: Linear Equations in Two Variables

Name: ______________________Date: __________________Score: ______ / 5

Section I: Key Formulas

Standard Form 2-Variable

ax + by + c = 0

Section II: Answer the Questions

1. Case Study - 1: On his birthday, Manoj planned that this time he celebrates his birthday in a small orphanage centre. He bought apples to give to children and adults working there. Manoj donated 2 apples to each children and 3 apples to each adult working there along with Birthday cake. He distributed 60 total apples. (a) Taking the number of children as ‘x’ and the number of adults as ‘y’. Represent the above situation in linear equation in two variables. (b) If the number of children is 15, then find the number of adults. (c) If the number of adults is 12, then find the number of children. (d) If x = -5 and y = 2 is a solution of the equation 3x + 5y = b, then find the value of ‘b’

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

2. Show that the points A (1, 2), B (-1, -16) and C (0, -7) lie on the graph of the linear equation y = 9x - 7.

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

3. How many linear equations in x and y can be satisfied by x = 1 and y = 2?

[ ] A. Only one[ ] B. Two[ ] C. Infinitely many[ ] D. Three

4. Any solution of the linear equation 2x + 0y = 9 in two variables, is of the form

[ ] A. 9 ,02 ( ) ( )( )[ ] B. 9 ,2 n( ) ( )( ) , n is a real number[ ] C. 9, 2n( ) ( )( ) , n is a real number[ ] D. 90, 2 ( ) ( )( )

5. If ΔACB ≅ ΔEDF, then which of the following equations is/are true? (I) AC = ED (II) ∠C = ∠F (III) AB = EF

[ ] A. Only[ ] B. [ ] C. [ ] D. All of these

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