Question

According to the Rational Root Theorem, -2/5 is a potential rational root of which function? ) = 4x4.72#*#25 O Foxo = 9x47x+10 OF) = 10x - 729 Fox) = 25x4.72​

Answer 1

Answer:

Option (4)

Step-by-step explanation:

Option (1)

f(x) = 4x⁴- 7x²+ x + 25

Possible rational roots will be,

$\frac{\pm \text{Factors of constant term '25'}}{{\pm \text{Factors of leading coefficient '4'}}}$

For the given function,

Possible rational roots = $\frac{\pm 1, 5, 25}{\pm 1,2}$

                                      = $\pm 1, \pm 5, \pm 25, \pm \frac{1}{2},\pm\frac{5}{2},\pm\frac{25}{2}$

Therefore, $-\frac{2}{5}$ is not the possible root.

Option (2)

f(x) = 9x⁴- 7x²+ x + 10

Possible rational roots = $\frac{\pm 1,\pm 2,\pm 5,\pm10}{\pm 1,\pm3,\pm9}$

Therefore, $-\frac{2}{5}$ is not the possible root.

Option (3)

f(x) = 10x⁴- 7x²+ x + 9

Possible rational roots = $\frac{\pm1, \pm3, \pm9}{\pm 1,\pm2,\pm5,\pm10}$

Therefore, $-\frac{2}{5}$ is not the possible root.

Option (4)

f(x) = 25x⁴- 7x²+ x + 4

Possible rational roots = $\frac{\pm 1,\pm2,\pm5}{\pm1,\pm5,\pm 25}$

                                      = $\pm1,\pm2,\pm5,\pm\frac{1}{5},\pm\frac{1}{25},\pm\frac{2}{5},\pm\frac{2}{25}$

Therefore, $-\frac{2}{5}$ is the possible rational root.

Option (4) will be the answer.