Class 10 Exercise 1.1 Quadratic Equation| X Ex 1.1 NEW Maths Federal Board National Book Foundation

Class 10 Exercise 1.1 Quadratic Equation| X Ex 1.1 NEW Maths Federal Board National Book Foundation
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1. Standard Form
• A quadratic equation is written as ax^2 + bx + c = 0.
2. Nature of Roots
• The discriminant D = b^2 - 4ac determines the type of roots:
3. Solution Techniques
• Factoring: Express the equation as a product of two binomials.
• Completing the Square: Rewriting the equation in the form (x + p)^2 = q.
• Quadratic Formula: Using the formula x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} to find the roots.
• Graphical Method: Solving by plotting the parabola and finding where it intersects the x-axis.
• Using Properties of Roots: Utilizing sum and product of roots based on Vieta’s formulas.
1. Write the following quadratic equations in standard form.
1. (x + 2)(x - 3) = 5
i.
. (x - 5) ^ 2 - (2x + 4) ^ 2 = 7
iii. x = x(x - 1)
ii Solve the equations by factorization 2.
(x - 1)(x - 4) = 0 x ^ 2 - 7x - 8 = 0
ii. x ^ 2 - 2x + 1 = 0
V. (2x + 7/4) ^ 2 = (48x ^ 2 + 529)/16
iv. x ^ 2 - 4x + 4 = (2x - 7) ^ 2
3. Solve the completing the square method.
1. x ^ 2 + 4x - 32 = 0
ii. x ^ 2 + 8x = 0
iii. x ^ 2 + 6x - 9 = 0
iv. 3x ^ 2 + 12x + 8 = 0
v. x ^ 2 + x + 1 = 0
vi. 4x ^ 2 - 8x - 5 = 0
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