Question

`F(x)=x^4-3x^3-7x^2-10x-25` `G(x)=x^4-4x^3+x^2-27x-15` Fidn the number of values o x for which `f(x)=g(x)=0`

Answer 1

`f(x) = g(x) = 0`
`=>f(x) - g(x) = 0`
`=>x^4-3x^3-7x^2-10x-25-x^4+4x^3-x^2+27x+15 = 0`
`=>x^3-8x^2+17x-10 = 0`
Now, if we put `x = 5` in the above polynomial,
`5^3-8(5)^2+17(5)- 10 = 0`
`=>125-200+85-10 = 0`
`=> 0 = 0`
So, `x = 5` satisfy the given condition.
So, this is the only value that satisfies `f(x) = g(x) = 0`.