Finding All Zeroes of a Polynomial Video Explanation Question Find all the zeroes of the polynomial \[ f(x) = 2x^4 – 9x^3 + 5x^2 + 3x – 1, \] if two of its zeroes are \(2+\sqrt{3}\) and \(2-\sqrt{3}\). Solution Step 1: Form the Quadratic Factor from the Given Zeroes Since the given zeroes are conjugates, […]
Finding All Zeroes of a Cubic Polynomial Video Explanation Question Find all the zeroes of the polynomial \[ f(x) = x^3 + 3x^2 – 2x – 6, \] if two of its zeroes are \( -\sqrt{2} \) and \( \sqrt{2} \). Solution Step 1: Form the Quadratic Factor from the Given Zeroes Since the given
Finding All Zeroes of a Cubic Polynomial Video Explanation Question Find all the zeroes of the polynomial \[ f(x) = 2x^3 + x^2 – 6x – 3, \] if two of its zeroes are \( -\sqrt{3} \) and \( \sqrt{3} \). Solution Step 1: Form the Quadratic Factor from the Given Zeroes Since the given
Finding All Zeroes of a Polynomial Video Explanation Question Find all the zeroes of the polynomial \[ f(x) = 2x^4 + 7x^3 – 19x^2 – 14x + 30, \] if two of its zeroes are \( \sqrt{2} \) and \( -\sqrt{2} \). Solution Step 1: Form the Quadratic Factor from the Given Zeroes Since the
Finding All Zeroes of a Polynomial Video Explanation Question Find all the zeroes of the polynomial \[ f(x) = x^4 + x^3 – 34x^2 – 4x + 120, \] if two of its zeroes are \(2\) and \(-2\). Solution Step 1: Form the Quadratic Factor from Given Zeroes Since \(2\) and \(-2\) are zeroes, \[
Finding All Zeroes of a Polynomial Video Explanation Question Find all the zeroes of the polynomial \[ f(x) = 2x^4 – 2x^3 – 7x^2 + 3x + 6, \] if two of its zeroes are \[ -\frac{\sqrt{3}}{2} \text{ and } \frac{\sqrt{3}}{2}. \] Solution Step 1: Form the Quadratic Factor from the Given Zeroes Since the
Finding All Zeroes of a Polynomial Video Explanation Question Obtain all the zeroes of the polynomial \[ f(x) = x^4 – 3x^3 – x^2 + 9x – 6, \] if two of its zeroes are \( -\sqrt{3} \) and \( \sqrt{3} \). Solution Step 1: Form the Quadratic Factor from Given Zeroes Since the zeroes
Finding All Zeroes of a Cubic Polynomial Video Explanation Question Obtain all the zeroes of the polynomial \[ f(x) = x^3 + 13x^2 + 32x + 20, \] if one of its zeroes is \(-2\). Solution Step 1: Use the Given Zero Since \(-2\) is a zero of the polynomial, \((x + 2)\) is a
Finding All Zeroes of a Polynomial Video Explanation Question Obtain all the zeroes of the polynomial \[ f(x) = 2x^4 + x^3 – 14x^2 – 19x – 6, \] if two of its zeroes are \(-2\) and \(-1\). Solution Step 1: Use the Given Zero \(x = -2\) Since \(-2\) is a zero, \((x +
Checking Factor Using Division Algorithm Video Explanation Question Check whether the first polynomial is a factor of the second polynomial: \[ g(x) = 2x^2 – x + 3, \quad f(x) = 6x^5 – x^4 + 4x^3 – 5x^2 – x – 15 \] Solution Step 1: Apply the Division Algorithm By the division algorithm, \[