Answer:
p(x) = x² - 2x -8
Step-by-step explanation:
We need to find the quadratic equation with roots 4 and -2 , we know that if a and ß are the roots of equⁿ , then the polynomial is ,
[tex]\implies p(x) =k[ x^2-(\alpha + \beta)x+\alpha\beta] [/tex]
Where k is constant . Substitute respective values ,
=> p(x) = k [ x² - ( a + ß )x + aß ]
=> p(x) = k [ x² - ( 4-2) x + (4)(-2) ]
=> p(x) = k [ x² -2x - 8 ]
If k = 1 ,
=> p(x) = x² - 2x - 8
