Use the Intermediate Value Theorem to show that there is a r

Use the Intermediate Value Theorem to show that there is a root of the given equation. x^4 + x - 3 = 0

1)given x⁴+x-3=0

let f(x)=x⁴+x-3

f(x) is polynomial , so it is continous

interval is not specified .

i take intervals (-2,0),(0,2)

for interval (-2,0)

f(-2) =16-2-3= 11

f(0)=0+0-3 =-3

f(0)< 0 <f(-2)

therefore by intermediate value theorem there exists c(-2,0) such that f(c)=0. so the equation has a root

for interval (0,2)

f(0)=0+0-3 =-3

f(2) =16+2-3= 15

f(0)< 0 <f(2)

therefore by intermediate value theorem there exists c(0,2) such that f(c)=0. so the equation has a root