Saved Bookmarks
| 1. |
verify that the numbers 3,1 ,- 1 are the zeros of the cubic polynomial x cube minus 4 x square + 5 x minus 2 also verify the relationship between the zeros and the coefficients |
|
Answer» We have,P(X)=3x 3 −5x 2 −11x−3And the zeros are 3,−1, 3−1 Verifying the zeros,x=3,p(3)=3(3) 3 −5(3) 2 −11(3)−3=81−45−33−3=0=x−1,p(−1)=3(−1) 3 −5(−1) 2 −11(−1)−3=−3−5+11−3=0x= 3−1 ,p( 3−1 )=3( 3−1 ) 3 −5( 3−1 ) 2 −11( 3−1 )−39−1 − 95 + 311 −39−1−5−33−27 0Now verifying the relation between zeros and COEFFICIENTS is:for,p(x)=3x 3 −5x 2 −11x−3a=3,b=−1,c=−11,d=−1and zeros α=3,β=−1γ= 3−1 Now,α+β+γ=3+(−1)+ 3−1 = 39−3−1 35 = a−b αβ+βγ+γα=(3)(−1)+(−1)( 3−1 )+( 3−1 )(3)3−9+1−3 = 3−11 = AC αβγ=(3)(−1)( 3−1 )1= AD Thus the relation are verified.Step-by-step explanation:your answer |
|