Question

if 2 and -2 are zeros of the polynomial p(x)=ax⁴ + 2x³ -3x² +bx -4,find the values of a and b.​

Answer 1

Answer:

a=-1,b=8

Step-by-step explanation:

a(2)^4+2(2)^3-3(2)^2+b(2)-4

16a+16-12+2b-4

16a+4+2b-4

16a+2b=0

(-2)^4+2(-2)^3-3(-2)^2+b(-2)-4

16a-16-12-2b-4

16a-28-2b-4

16a-32-2b

By adding 2 and 3rd equation,

16a+2b=0

16a-32-2b=0

- +

-32+4b=0

4b=32

b=32

4

b=8

By substituting b=8 in equation,

16a+2(8)=0

16a+16=0

16a=-16

a=-16

16

a=-1

Answer 2

Answer:

Let f(x) = ax4 +2x3 -3x2 +bx -4 and g(x) = x2 -4 We have g(x) = x2 − 4 = (x-4) (x+2) Given g(x) is a factor of f(x). (x-2) and (x+2) are factors of f(x) From factor theorem, If (x-2) and (x+2) are factor of f(x) then f(2) = 0 and f(-2) = 0 respectivelyRead more on Sarthaks.com - https://www.sarthaks.com/107013/find-the-values-of-a-and-b-if-x-2-4-is-a-factor-of-ax-4-2x-3-3x-2-bx-4

Step-by-step explanation:

hope it helps you