Find a polynomial of the specified degree that satisfies the given conditions. Degree 4; zeros -1, 1, square root of 6 ; integer coefficients and constant term 12

Question

Kali Galloway · Accepted Answer

Step 1Since irrational zeros occur in pairs,the zeros of the required polynomial are,  −  1  ,  1  ,      6    ,  −      6  So, the polynomial is,  p  (  x  )  =  a  (  x  +  1  )  (  x  −  1  )  (  x  −      6    )  (  x  +      6    )  p  (  x  )  =  a  (      x    2    −  1  )  (      x    2    −  6  )  p  (  x  )  =  a  (      x    4    −  7      x    2    +  6  )  p  (  x  )  =  a      x    4    −  7  a      x    2    +  6  a  →  (  1  )Step 2They said constant term   =  12  6  a  =  12  a  =  2Substitute in (1),  p  (  x  )  =  2      x    4    −  14      x    2    +  12

Find a polynomial of the specified degree that satisfies the given conditions. Degree 4; zeros -1, 1, square root of 6 ; integer coefficients and constant term 12

Answered question

Answer & Explanation

New Questions in Pre-Algebra