Question

if 2,3are the zeroes of the polynomial g(y) = y^4 _ ay^3 + 37y^2 +by + 36 ,find the value of a and b.​

Answer 1

Answer:

Step-by-step explanation:

Let f(x)=x4−6x3−26x2+138x−35.

Let α=(2+3–√)andβ=(2−3–√). Then,

(α+β)=4andαβ=(4−3)=1.

So, the quadratic polynomial whose roots are αandβ is given by

x2−(α+β)x+αβ=(x2−4x+1).

∴(x2−4x+1) is a factor of f(x).

On dividing f(x) by (x2−4x+1), we get

∴f(x)=(x2−4x+1)(x2−2x−35).

∴ the other two zeros of f(x) are given by (x2−2x−35)=0.

Now, x2−2x−35=0⇒x2−7x+5x−35=0

⇒x(x−7)+5(x−7)=0

⇒(x−7)(x+5)=0

⇒x−7=0orx+5=0

⇒x=7orx=−5.

Hence, the other two zeros of f(x) are 7 and -5.