Question

obtain all other zeros of the polynomial x^4-17x^4-36x=20 if two of its zeros are +5 and -2​

Answer 1

Step-by-step explanation:

Solution :

$p(x) = {x}^{4} - 17 {x}^{2} - 36x - 20$

Let its root be α, β, 5 and -2.

$comaring \: p(x)with \: ax ^{4} + {bx}^{3} + {cx}^{2} + dx + e$

We get,

a = 1, b = 0, c = -17, d = -36, e = -20

Now :

$\alpha + \beta + 5 + ( - 2) = \frac{ - p}{ \alpha } = 0$

=> α + β + 5 + (-2) = -p/α –––(A)

And products of roots, αβ × 5 × -2 = e/α = -20

=> αβ = 2 –––(B)

From (A) and (B), we get that α and β are -1 and -2

Hence :

Zero of given polynomial are 5, -1, -2, -2.