Nature of Pair of Linear Equations Using Ratio of Coefficients Video Explanation Question On comparing the ratios \[ \frac{a_1}{a_2}, \frac{b_1}{b_2}, \frac{c_1}{c_2}, \] find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide (without drawing them): (i) \(5x – 4y + 8 = 0,\; 7x + […]

Graphical Representation Using Ratio of Coefficients Video Explanation Question Gloria is walking along the path joining the points \((-2, 3)\) and \((2, -2)\), while Suresh is walking along the path joining \((0, 5)\) and \((4, 0)\). Represent this situation graphically and check the nature of the paths using the ratio of coefficients. Solution Step 1:

Graphical Representation of the Paths of Two Trains Video Explanation Question The path of train A is given by the equation \[ 3x + 4y – 12 = 0 \] and the path of another train B is given by \[ 6x + 8y – 48 = 0. \] Represent this situation graphically. Solution Step

Linear Equations in Two Variables – Algebraic and Graphical Representation Video Explanation Question Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Represent this situation algebraically and graphically. Solution Step 1:

Algebraic and Graphical Representation Using Linear Equation in Two Variables Video Explanation Question Akhila went to a fair in her village. She enjoyed rides on the Giant Wheel and played Hoopla. The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. Each ride costs ₹3 and

Verify that 1/2, 1 and −2 are the zeroes of the cubic polynomial f(x) = 2x³ + x² − 5x + 2 and verify the relationship between the zeroes and coefficients Video Explanation Watch the video explanation below: Given f(x) = 2x³ + x² − 5x + 2 The given zeroes are: 1/2, 1 and

Graph of a Quadratic Polynomial Video Explanation Question Which of the following is not the graph of a quadratic polynomial? Solution Key Property of a Quadratic Polynomial The graph of a quadratic polynomial \[ f(x) = ax^2 + bx + c \] is always a parabola which: opens upward or downward has exactly one turning

Quadratic Polynomial with Opposite Zeroes Video Explanation Question If one of the zeroes of a quadratic polynomial of the form \[ x^2 + ax + b \] is the negative of the other, then it: (a) has no linear term and constant term is negative (b) has no linear term and the constant term is

Equal Zeroes of a Quadratic Polynomial Video Explanation Question If the zeroes of the quadratic polynomial \[ f(x) = ax^2 + bx + c, \quad c \neq 0 \] are equal, then: (a) \(c\) and \(a\) have opposite signs (b) \(c\) and \(b\) have opposite signs (c) \(c\) and \(a\) have the same sign (d)

Finding the Value of k Using Zero of a Polynomial Video Explanation Question If one zero of the quadratic polynomial \[ f(x) = x^2 + 3x + k \] is \(2\), find the value of \(k\). Options: (a) 10    (b) -10    (c) 5    (d) -5 Solution Step 1: Use the Zero Condition