Question

Find all rational zeros of the polynomial
P(x)= 2 x^4 + 7 x^3 - 13 x^2 + 7 x - 15

x1 ≤ x2 ≤ x3 ≤ x4

Answer 1

\[\huge\rm \frac{ p }{ q } \]method to find rational zeros
where p is factor of constant term
and q is factor of leading coefficient

Answer 2

leading coefficient is 2
so i would replace q with factors of 2
\[\huge\rm \frac{ p }{ \pm1 , \pm 2 }\]
write factors of constant term at the numerator :=))
leading coefficient is 2 and rational zero must be the divisor of constant term
you should test these numbers to find zero
replace x with each number into the equation if you get 0 then then u substituted would be the answer :=)

Answer 3

here is an example f(x)= 2x^3 +3x^2 +4
use the p/q expression \[\rm \frac{ factors ~of ~constant~term }{factors~of~leading~coefficeint }\]

leading coefficient is 2
constant term 4 \[\frac{ \pm1 ,\pm 2 \pm 4 }{ \pm 1, \pm 2 }\]
so possible rational zeros are
after finding possible rational zero i can test each number by plugging them into the original equation
f(1)=2(1)^3+3(1)^2+4
f(2)=2(2)2+3(2)^2+4
same with other 3 options