Exercise 2.3 Math 10th FBISE(Islamabad) new course NBF based on SNC2022| 10th Math Ex 2.3 unit 2

Описание: ​In this video, we dive deep into Unit 2: Quadratic Equations, specifically focusing on Exercise 2.3 from the New Course of Class 10 Mathematics based on the latest National Book Foundation (NBF) textbook for the Federal Textbook Board (Islamabad), aligned with the Single National Curriculum (SNC) 2022-2023.
​🔍 What You Will Learn:
​In this lesson, we cover the fundamental concepts of quadratic equations, including:
Exercise 2.3
Question 1:
​Find the discriminant of the following quadratic equations.
​(i) x^2 + 6x - 27 = 0
​(ii) x^2 - x - 12 = 0
​(iii) 8x^2 + 2x + 1 = 0
​(iv) 12x^2 - 11x - 15 = 0
Question 2:
​Discuss the nature of roots of the following quadratic equations.
​(i) x^2 - 2x - 15 = 0
​(ii) x^2 + 3x - 4 = 0
​(iii) 12x^2 + x - 20 = 0
​(iv) x^2 + 2x + 8 = 0
​(v) x^2 + 3x - 9 = 0
Question 3:
​For what value of k, 9x^2 - kx + 16 = 0 is a perfect square?
Question 4: ​If roots of x^2 + kx + 9 = 0 are equal, find k?
Question 5: ​Show that the roots of 2x^2 + (mx - 1)^2 = 3, are equal if 3m^2 + 4 = 0.
Question 6:
Find the value of "m" when roots of the following quadratic equations are equal.
​(i) x^2 - 6x + m = 0
​(ii) m^2x^2 + (2m + 1)x + 1 = 0
​(iii) (m + 3)x^2 + (m + 1)x + m + 1 = 0
Question 7:
Show that the roots of the equation (a^2 + b^2)x^2 + 2(ac + bd)x + c^2 + d^2 = 0 are imaginary. Moreover, it shows repeated roots if ad = bc.
Question 8:
Show that the roots of the equation (ax + c)^2 = 4bx will be equal, if b = ac.
Question 9
Show that the roots of the following equations are real.
​(i) mx^2 - 2mx + m - 1 = 0
​(ii) bx^2 + ax + a - b = 0
Question 10:
Show that the roots of the following equation are real.
(a + b)x^2 - ax - b = 0
​📚 Book Details:
​Subject: Mathematics (Grade 10)
​Unit: 2 (Theory of Quadratic Equations)
Exercise 2.3
​Publisher: National Book Foundation (NBF)
​Board: Federal Board (FBISE) Islamabad
​Curriculum: Single National Curriculum (2022-2023 onwards.
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