Evaluation of \( \dfrac{1}{\alpha} – \dfrac{1}{\beta} \) Video Explanation Question If \( \alpha \) and \( \beta \) are the zeroes of the quadratic polynomial \[ f(x) = ax^2 + bx + c, \] evaluate \[ \frac{1}{\alpha} – \frac{1}{\beta}. \] Solution Step 1: Use Relations Between Zeros and Coefficients For the quadratic polynomial \( ax^2 […]
Evaluation of \( \alpha – \beta \) Video Explanation Question If \( \alpha \) and \( \beta \) are the zeroes of the quadratic polynomial \[ f(x) = ax^2 + bx + c, \] evaluate \( \alpha – \beta \). Solution Step 1: Write Relations Between Zeros and Coefficients For the quadratic polynomial \( ax^2
Polynomial from Transformed Zeros Video Explanation Question If \( \alpha \) and \( \beta \) are the zeros of the quadratic polynomial \[ f(x) = x^2 – 2x + 3, \] find a polynomial whose roots are \[ \frac{\alpha – 1}{\alpha + 1} \quad \text{and} \quad \frac{\beta – 1}{\beta + 1}. \] Solution Step 1:
Polynomial from Given Zeros Video Explanation Question If \( \alpha \) and \( \beta \) are the zeros of the quadratic polynomial \[ f(x) = x^2 – 2x + 3, \] find a polynomial whose zeros are \[ \alpha + 2 \quad \text{and} \quad \beta + 2. \] Solution Step 1: Find Sum and Product
Polynomial from Given Zeros Video Explanation Question If \( \alpha \) and \( \beta \) are the zeros of the polynomial \[ f(x) = x^2 + px + q, \] form a polynomial whose zeros are \[ (\alpha + \beta)^2 \quad \text{and} \quad (\alpha – \beta)^2. \] Solution Step 1: Write Relations Between Zeros and
Quadratic Polynomial from Given Zeros Video Explanation Question If \( \alpha \) and \( \beta \) are the zeros of the quadratic polynomial \[ f(x) = x^2 – 3x – 2, \] find a quadratic polynomial whose zeros are \[ \frac{1}{2\alpha + \beta} \quad \text{and} \quad \frac{1}{2\beta + \alpha}. \] Solution Step 1: Find \(
Quadratic Polynomial from Given Zeros Video Explanation Question If \( \alpha \) and \( \beta \) are the zeros of the quadratic polynomial \[ f(x) = x^2 – 1, \] find the quadratic polynomial whose zeros are \[ \frac{2\alpha}{\beta} \quad \text{and} \quad \frac{2\beta}{\alpha}. \] Solution Step 1: Find Sum and Product of \( \alpha \)
Quadratic Polynomial from Given Zeros Video Explanation Question If \( \alpha \) and \( \beta \) are the zeros of a quadratic polynomial such that \[ \alpha + \beta = 24 \quad \text{and} \quad \alpha – \beta = 8, \] find a quadratic polynomial having \( \alpha \) and \( \beta \) as its zeros.
Proof Using Zeros of a Quadratic Polynomial Video Explanation Question If \( \alpha \) and \( \beta \) are the zeros of the quadratic polynomial \[ f(x) = x^2 – p(x + 1) – c, \] show that \[ (\alpha + 1)(\beta + 1) = 1 – c. \] Solution Step 1: Write the Polynomial
Proof Using Zeros of a Quadratic Polynomial Video Explanation Question If \( \alpha \) and \( \beta \) are the zeros of the quadratic polynomial \[ f(x) = x^2 – px + q, \] prove that \[ \frac{\alpha^2}{\beta^2} + \frac{\beta^2}{\alpha^2} = \frac{p^4}{q^2} – \frac{4p^2}{q} + 2. \] Solution Step 1: Write Relations Between Zeros and