Saved Bookmarks
| 1. |
PN,I c and B are the zeroes of the polynomi32?_72-6. find a Polynomial whase IHeroes are 28 +33 and 30 +23. |
|
Answer» α² + β² can be written as (α + β)² - 2αβ p(x) = 3x² - 7x + 6a = 3 , b = - 7 , c = 6 α and β are the zeros of p(x) we know that ,sum of zeros = α + β = -b/a = 7/3product of zeros =c/a = 6/3 = 22α + 3β and 3α + 2β are zeros of a polynomial. sum of zeros = 2α + 3β+ 3α + 2 = 5α + 5β= 5 [ α + β]= 5 × 7/3 = 35/3product of zeros = (2α + 3β)(3α + 2β)= 2α [ 3α + 2β] + 3β [3α + 2β]= 6α² + 4αβ + 9αβ + 6β²= 6α² + 13αβ + 6β²= 6 [ α² + β² ] + 13αβ = 6 [ (α + β)² - 2αβ ] + 13αβ = 6 [ ( 7/3)² - 2 × 3 ] + 13× 2= 6 [ 49/9 - 6 ] +26 = 6 [ 49/9 – 54/9] + 26 = 204/9 = 68/3[ simplest form ] a quadratic polynomial is given by :-k { x² - (sum of zeros)x + (product of zeros) }k {x² - 35/3x + 68/3}k = 22 {x² - 35/3x + 68/3 ]=6x² - 35x + 68 is the required polynomial |
|