Finding the Third Zero of a Cubic Polynomial Video Explanation Question If two zeroes of the polynomial \[ f(x) = x^3 + x^2 – 9x – 9 \] are \(3\) and \(-3\), find its third zero. Options: (a) -1 (b) 1 (c) -9 (d) 9 Solution Step 1: Use the Formula for […]
If Two Zeroes of the Polynomial x³ + x² − 9x − 9 Are 3 and −3, Find Its Third Zero Read More »
Finding a Quadratic Polynomial from Given Zeroes Video Explanation Question A quadratic polynomial, the sum of whose zeroes is \(0\) and one zero is \(3\), is: (a) \(x^2 – 9\) (b) \(x^2 + 9\) (c) \(x^2 + 3\) (d) \(x^2 – 3\) Solution Step 1: Find the Other Zero Let the zeroes
A Quadratic Polynomial Whose Sum of Zeroes Is 0 and One Zero Is 3 Read More »
Making a Given Number a Zero of a Polynomial Video Explanation Question What should be subtracted from the polynomial \[ f(x) = x^2 – 16x + 30 \] so that \(15\) is a zero of the resulting polynomial? Options: (a) 30 (b) 14 (c) 15 (d) 16 Solution Step 1: Use the
Making a Given Number a Zero of a Polynomial Video Explanation Question What should be added to the polynomial \[ f(x) = x^2 – 5x + 4 \] so that \(3\) is a zero of the resulting polynomial? Options: (a) 1 (b) 2 (c) 4 (d) 5 Solution Step 1: Use the
Product of Zeroes of a Cubic Polynomial Video Explanation Question The product of the zeroes of the polynomial \[ f(x) = x^3 + 4x^2 + x – 6 \] is: (a) -4 (b) 4 (c) 6 (d) -6 Solution Step 1: Use the Formula for Product of Zeroes For a cubic polynomial
The Product of the Zeros of the Polynomial x³ + 4x² + x − 6 Read More »
Finding the Third Zero of a Cubic Polynomial Video Explanation Question If two zeroes of the polynomial \[ f(x) = x^3 + x^2 – 5x – 5 \] are \( \sqrt{5} \) and \( -\sqrt{5} \), find its third zero. Options: (a) 1 (b) -1 (c) 2 (d) -2 Solution Step 1:
If Two Zeros of the Polynomial x³ + x² − 5x − 5 Are √5 and −√5, Find Its Third Zero Read More »
Finding the Third Zero of a Cubic Polynomial Video Explanation Question If two of the zeroes of the cubic polynomial \[ f(x) = ax^3 + bx^2 + cx + d \] are each equal to zero, find the third zero. Solution Step 1: Use the Product of Zeroes Formula For a cubic polynomial \[ ax^3
Evaluation Using Zeros of a Quadratic Polynomial Video Explanation Question If \( \alpha \) and \( \beta \) are the zeroes of the polynomial \[ f(x) = ax^2 + bx + c, \] find \[ \frac{1}{\alpha^2} + \frac{1}{\beta^2}. \] Solution Step 1: Write Relations Between Zeroes and Coefficients For the quadratic polynomial \(ax^2 + bx
Evaluation Using Zeros of a Cubic Polynomial Video Explanation Question If \( \alpha, \beta, \gamma \) are the zeroes of the polynomial \[ f(x) = x^3 – px^2 + qx – r, \] find \[ \frac{1}{\alpha\beta} + \frac{1}{\beta\gamma} + \frac{1}{\gamma\alpha}. \] Solution Step 1: Write Relations Between Zeroes and Coefficients For the cubic polynomial \(x^3
Evaluation Using Zeros of a Cubic Polynomial Video Explanation Question If \( \alpha, \beta, \gamma \) are the zeroes of the polynomial \[ f(x) = ax^3 + bx^2 + cx + d, \] find \[ \alpha^2 + \beta^2 + \gamma^2. \] Solution Step 1: Write Relations Between Zeroes and Coefficients For the cubic polynomial \(