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
Condition on Zeros of a Quadratic Polynomial Video Explanation Question If the squared difference of the zeros of the quadratic polynomial \[ f(x) = x^2 + px + 45 \] is equal to \(144\), find the value of \(p\). Solution Step 1: Write Relations Between Zeros and Coefficients Let the zeros be \( \alpha \)
Value of an Expression Using Zeros of a Quadratic Polynomial Video Explanation Question If \( \alpha \) and \( \beta \) are the zeros of the quadratic polynomial \[ p(s) = 3s^2 – 6s + 4, \] find the value of \[ \frac{\alpha}{\beta} + \frac{\beta}{\alpha} + 2\left(\frac{1}{\alpha} + \frac{1}{\beta}\right) + 3\alpha\beta. \] Solution Step 1:
Value of an Expression Using Zeros of a Quadratic Polynomial Video Explanation Question If \( \alpha \) and \( \beta \) are the zeros of the quadratic polynomial \[ f(x) = 6x^2 + x – 2, \] find the value of \[ \frac{\alpha}{\beta} + \frac{\beta}{\alpha}. \] Solution Step 1: Use Relations Between Zeros and Coefficients
If α and β are the zeros of the quadratic polynomial f(t) = t² − 4t + 3, find the value of (α⁴β³ + α³β⁴) Video Explanation Watch the video explanation below: Solution Given polynomial: f(t) = t² − 4t + 3 Step 1: Find α + β and αβ Comparing f(t) = t² −
Value of an Expression Using Zeros of a Quadratic Polynomial Video Explanation Question If \( \alpha \) and \( \beta \) are the zeros of the quadratic polynomial \[ p(x) = 4x^2 – 5x – 1, \] find the value of \[ \alpha^2\beta + \alpha\beta^2. \] Solution Step 1: Use Relations Between Zeros and Coefficients
Condition on Zeros of a Quadratic Polynomial Video Explanation Question If the sum of the zeroes of the quadratic polynomial \[ f(t) = kt^2 + 2t + 3k \] is equal to their product, find the value of \(k\). Solution Step 1: Write the Relations Between Zeros and Coefficients For a quadratic polynomial \(at^2 +