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Chapter 5: Quadratic Equations

    Introduction

    Quadratic Equations

    Solution of a Quadratic Equation by Factorisation

    Solution of a Quadratic Equation by Completing the square

    Nature of Roots

    Summary

    Enhanced Curriculum Support

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 5: Quadratic Equations > Enhanced Curriculum Support

Enhanced Curriculum Support

This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:

Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.

Exam Preparedness: Sample Question Papers provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.

Sample Questions

About the Section

Sec A

(1) "The product of two consecutive positive integers is 30". This can be expressed algebraically as .....

(A) x (x + 2) = 30 (B) x (x - 2) = 30 (C) x (x - 3) = 30 (D) x (x + 1) = 30

(2) Which of the following equation has '2' as a root?

(A) x2 - 4x + 5 = 0 (B) x2 + 3x - 12 = 0

(C) 2x2 - 7x + 6 = 0 (D) 3x2 - 6x - 2 = 0

(3) Find the discriminant of quadratic equation x2−5x+6 = 0.

(4) The quadratic equation with roots 2+3 and 2−3 is .....

(A) x2 + 4x + 1 = 0 (B) x2 + 4x - 1 = 0

(C) x2 - 4x + 1 = 0 (D) x2 - 4x - 1 = 0

(5) The Quadratic equation, whose sum of the roots is -3 and product of the roots is 2.

(A) x2 + 6x + 5 = 0 (B) x2 - x - 6 = 0 (C) x2 - 3x + 2 = 0 (D) x2 + 3x + 2 = 0

(6) The roots of a Quadratic equation 2x2 + x + 4 = 0 are ......

(A) One is positive and other is negative. (B) Both are positive. (C) Both are negative. (D) No real roots.

(7) Find the roots of the Quadratic equation x2+2x−3 = 0.

(8) Find the roots of the Quadratic equation x2 + 2x - 3 = 0.

(9) Find sum and product of roots of the Quadratic equation: x2−43x+9 = 0

Sec B

(1) Construct a Quadratic equation having the roots log28 and log10100.

(2) Solve the quadratic equation: 2sin2θ−3sinθ+1=0, where 0° < θ ≤ 90°.

(3) Write a Quadratic equation whose roots are the values of sin 30° and cos 60°.

(4) Write the Quadratic equation, whose roots are 2+3 and 2−3.

(5) Is x+22 = x2 + 3 a Quadratic equation ? Justify.

(6) Write the Quadratic equation, whose roots are 2+3 and 2−3.

(7) If the equation kx2 - 2kx + 6 = 0 has equal roots, then find the value of k.

Sec C

(1) Sum of the areas of two squares is 850 m2. If the difference of their perimeters is 40 m. Find the sides of the two squares.

(2) Sum of the present ages of two friends are 23 years, five years ago product of their ages was 42. Find their ages 5 years hence.

(3) Sum of the areas of two squares is 850 m2. If the difference of their perimeters is 40 m, find the sides of the two squares.

(4) Sum of the present ages of two friends are 23 years, five years ago product of their ages was 42. Find their ages 5 years hence.

(5) Write a Quadratic equation, whose roots are 3+5 and 3−5.

(6) Sum of squares of two consecutive even numbers is 580. Find the numbers by writing a suitable Quadratic equation.

Sec D

(1) Find the roots of the quadratic equation x2 + 3x - 18 = 0 by the method of completing the square.