Question

if one of the zeros of polynomial f(x)=(k^2+8)x^2+13x+6k is reciprocal of the other, then k is​

Answer 1

Answer:

4 and 2

Step-by-step explanation:

We know polynomials written in the form of ax^2 + bx + c represent -b/a as sum of their roots and c/a as product of their roots.

 Here,

⇒ c = 6k  and a = k^2 + 8

  As both are reciprocal of each other:

⇒ Their product = 1

⇒ c/a = 1

⇒ 6k / ( k^2 + 8 ) = 1

⇒ 6k = k^2 + 8

⇒ k^2 - 6k + 8 = 0

        ⇒ k^2 - 4k - 2k + 8 = 0

        ⇒ k( k - 4 ) - 2( k - 4 ) = 0

        ⇒ ( k - 4 )( k - 2 ) = 0

Hence the possible values of k are 4 and 2.

Answer 2

Answer:

answer is in the attachment

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