Question

in each of the two following polynomials, find the value of a, if ×-a is a factor of (i) ×3-a×2-2×+a+4. (ii) ×4-a2×2+3×-a ​

Answer 1

Answer:

i) a = $\frac{-4}{3}$

ii) a = 0

Step-by-step explanation:

i) f(x) = x³ + ax² + (- 2x + a) + 4 = 0

By factor theorem, if x+a is a factor of f(x), then f (−a) = 0

∴ f (−a) = 0

f(−a) ⇒ (−a)³ +a(−a)² −2(−a) + a = −4

       ⇒ (−a)³ + (a)³ +2a + a = −4

       ⇒ 3a = −4

       ⇒ a = $\frac{-4}{3}$

ii) f(x) = x⁴  − a²x²  + 3x − a

By factor theorem, if x+a is a factor of f(x) then f (−a) = 0

f(−a) ⇒ (−a)⁴  − a²(−a)² +3(−a) − a = 0  

       ⇒ a⁴  − a⁴ − 3a − a = 0

       ⇒ −4a = 0

       ⇒ a = 0