Quadratic Equations and Linear Inequalities — Chapter Summary
NIOS · Class 12 · Mathematics
Summary of Quadratic Equations and Linear Inequalities for NIOS Class 12 Mathematics. Part of the NIOS Class 12 Mathematics syllabus.
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Overview
This chapter covers two fundamental topics in algebra: quadratic equations and linear inequalities. Quadratic equations are polynomial equations of degree 2, expressed in the standard form ax² + bx + c = 0 (where a ≠ 0), which have applications throughout mathematics, physics, and engineering. Linea
Key Concepts
A polynomial equation of the second
A polynomial equation of the second degree written as ax² + bx + c = 0, where a ≠ 0. Here, 'a' is the leading coefficient (coefficient of x²), 'b' is
A value
A value that, when substituted for the variable in an equation, makes the equation true (satisfies it). For a quadratic equation ax² + bx + c = 0, if
A technique to solve quadratic equations
A technique to solve quadratic equations by expressing the quadratic expression as a product of two linear factors. Steps: (1) Write the equation ax²
A universal formula to find roots
A universal formula to find roots of any quadratic equation ax² + bx + c = 0: x = (-b ± √D) / (2a), where D = b² - 4ac is the discriminant. This formu
The expression D = b²
The expression D = b² - 4ac under the square root in the quadratic formula that determines the nature of roots. If D > 0, the equation has two real an
Learning Objectives
- Solve quadratic equations using factorization method
- Apply the quadratic formula to find roots of any quadratic equation
- Examine the nature of roots using the discriminant (D = b² - 4ac)
- Establish and apply relationships between roots and coefficients (sum and product of roots)
- Form quadratic equations when roots are given
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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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