Question

If one zero of the polynomial [a^2+9]x^2+13x+6a is reciprocal of the other find value of a

Answer 1

Answer:

Step-by-step explanation:

If one of the zero is reciprocal of the other, 

let one zero be α

other zero will be 1/α

Product of roots = c/a

⇒ α × 1/α = 6a/(a²+9)

⇒ 1 = 6a/(a²+9)

⇒ a² + 9 = 6a

⇒ a² - 6a + 9 = 0

⇒ a² - 3a - 3a + 9= 0

⇒ a(a-3) -3(a-3) = 0

⇒ (a-3)(a-3) = 0

⇒ (a-3)²= 0

⇒ a = 3

Value of a is 3.

Answer 2

Answer:

Step-by-step explanation:

Mark me brainliest Hala Madrid BAL

polynomial is (a2+9)x2 + 13x + 6a

Let one zero be b then other zero will be reciprocal of it i.e.1/b.

∴ product of the zeroes = constant term/cofficient of x2 = 1 (as b*1/b = 1)

6a/(a2+9) = 1

⇒ 6a = a2+9

⇒ a2 -6a + 9 = 0

⇒ (a-3)2 = 0

⇒ a - 3 = 0

⇒ a = 3

polynomial will be (32+9)x2 + 13x + 6*3  

= 18x2 + 13x + 18

This polynomial will be have imaginary roots because b2-4ac<0