If α and β are the zeros of the polynomial f(x) = x² + px + q, find the polynomial whose zeros are (α + β)² and (α − β)² Video Explanation Watch the video explanation below: Solution Given polynomial: f(x) = x² + px + q Let α and β be the zeros of […]

If α and β are the zeros of the quadratic polynomial f(x) = x² − 3x − 2, find the quadratic polynomial whose zeros are 1/(2α + β) and 1/(2β + α) Video Explanation Watch the video explanation below: Solution Given polynomial: f(x) = x² − 3x − 2 Step 1: Find α + β

If α and β are the zeros of the quadratic polynomial f(x) = x² − 1, find the quadratic polynomial whose zeros are 2α/β and 2β/α Video Explanation Watch the video explanation below: Solution Given polynomial: f(x) = x² − 1 Step 1: Find α + β and αβ Comparing f(x) = x² − 1

If α and β are the zeros of a quadratic polynomial such that α + β = 24 and α − β = 8, find a quadratic polynomial having α and β as its zeros Video Explanation Watch the video explanation below: Solution Given: α + β = 24 α − β = 8 Step

If α and β are the zeros of the quadratic polynomial f(x) = x² − p(x + 1) − c, show that (α + 1)(β + 1) = 1 − c Video Explanation Watch the video explanation below: Proof Given polynomial: f(x) = x² − p(x + 1) − c Simplifying the polynomial: f(x) =

If α and β are the zeros of the quadratic polynomial f(x) = x² − px + q, prove that α²/β² + β²/α² = p⁴/q² − 4p²/q + 2 Video Explanation Watch the video explanation below: Proof Given polynomial: f(x) = x² − px + q Let α and β be the zeros of the

If the squared difference of the zeros of the quadratic polynomial f(x) = x² + px + 45 is equal to 144, find the value of p Video Explanation Watch the video explanation below: Solution Given polynomial: f(x) = x² + px + 45 Step 1: Find α + β and αβ Let the zeros

If α and β are the zeros of the quadratic polynomial p(s) = 3s² − 6s + 4, find the value of α/β + β/α + 2(1/α + 1/β) + 3αβ Video Explanation Watch the video explanation below: Solution Given polynomial: p(s) = 3s² − 6s + 4 Step 1: Find α + β and

If α and β are the zeros of the quadratic polynomial f(x) = 6x² + x − 2, find the value of (α/β + β/α) Video Explanation Watch the video explanation below: Solution Given polynomial: f(x) = 6x² + x − 2 Step 1: Find α + β and αβ Comparing f(x) = 6x² +

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 −