Value of an Expression Using Zeros of a Quadratic Polynomial Video Explanation Question If \( \alpha \) and \( \beta \) are the zeros of the quadratic polynomial \[ f(x) = x^2 – 5x + 4, \] find the value of \[ \frac{1}{\alpha} + \frac{1}{\beta} – 2\alpha\beta. \] Solution Step 1: Find the Zeros of […]
If α and β Are the Zeros of f(x) = x² − 5x + 4, Find the Value of 1/α + 1/β − 2αβ Read More »
Quadratic Polynomial from Given Zeros Video Explanation Question Find a quadratic polynomial whose sum and product of the zeros are: \[ \text{Sum} = -\frac{3}{2\sqrt{5}}, \quad \text{Product} = -\frac{1}{2} \] Also, find the zeros of this polynomial by factorisation. Solution Step 1: Use the Standard Form If the sum of zeros is \(S\) and the product
Quadratic Polynomial from Given Zeros Video Explanation Question Find a quadratic polynomial whose sum and product of the zeros are: \[ \text{Sum} = -2\sqrt{3}, \quad \text{Product} = -9 \] Also, find the zeros of this polynomial by factorisation. Solution Step 1: Use the Standard Form If the sum of zeros is \(S\) and the product
Quadratic Polynomial from Given Zeros Video Explanation Question Find a quadratic polynomial whose sum and product of the zeros are \[ \text{Sum} = \frac{21}{8}, \quad \text{Product} = \frac{5}{16} \] Also, find the zeros of this polynomial by factorisation. Solution Step 1: Write the General Form If the sum of zeros is \(S\) and the product
Quadratic Polynomial from Given Zeros Video Explanation Question Find a quadratic polynomial whose sum and product of the zeros are \[ \text{Sum} = -\frac{8}{3}, \quad \text{Product} = \frac{4}{3} \] Also, find the zeros of this polynomial by factorisation. Solution Step 1: Write the General Form of the Quadratic Polynomial If the sum of zeros is
Zeros of a Quadratic Polynomial Video Explanation Question Find the zeros of the quadratic polynomial \[ q(y) = 7y^2 – \frac{11}{3}y – \frac{2}{3} \] and verify the relationship between the zeros and their coefficients. Solution Step 1: Remove Fractions Multiply the polynomial by 3: \[ 3q(y) = 21y^2 – 11y – 2 \] Step 2:
Zeros of a Quadratic Polynomial Video Explanation Question Find the zeros of the quadratic polynomial \[ p(y) = y^2 + \frac{3\sqrt{5}}{2}y – 5 \] and verify the relationship between the zeros and their coefficients. Solution Step 1: Remove the Fraction Multiply the polynomial by 2: \[ 2y^2 + 3\sqrt{5}y – 10 \] Step 2: Factorise
Zeros of a Quadratic Polynomial Video Explanation Question Find the zeros of the quadratic polynomial \[ f(v) = v^2 + 4\sqrt{3}v – 15 \] and verify the relationship between the zeros and their coefficients. Solution Step 1: Factorise the Polynomial Given: \[ f(v) = v^2 + 4\sqrt{3}v – 15 \] Product of the coefficient of
Zeros of a Quadratic Polynomial Video Explanation Question Find the zeros of the quadratic polynomial \[ h(s) = 2s^2 – (1 + 2\sqrt{2})s + \sqrt{2} \] and verify the relationship between the zeros and their coefficients. Solution Step 1: Factorise the Polynomial Given: \[ h(s) = 2s^2 – (1 + 2\sqrt{2})s + \sqrt{2} \] Product
Zeros of a Quadratic Polynomial Video Explanation Question Find the zeros of the quadratic polynomial \[ g(x) = a(x^2 + 1) – x(a^2 + 1) \] and verify the relationship between the zeros and their coefficients. Solution Step 1: Write the Polynomial in Standard Form \[ g(x) = ax^2 + a – (a^2 + 1)x