if one of the zero polynomial f x is equals to 5 x square + 13 x + K is reciprocal of other then find value of k
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Sol:
Let the roots of (k2 + 4) x2 + 13x + 4k be p and 1/p.
Product of the roots = p x 1/p = (constant term) / coefficient of x2
⇒ (4k) / (k2 + 4) = p x 1/p
⇒ (4k) / (k2 + 4) = 1
⇒ k2 - 4k + 4 = 0
⇒ (k - 2)2 = 0
⇒ k - 2 = 0
⇒ k = 2
Therefore, the value of k is 2.
Let the roots of (k2 + 4) x2 + 13x + 4k be p and 1/p.
Product of the roots = p x 1/p = (constant term) / coefficient of x2
⇒ (4k) / (k2 + 4) = p x 1/p
⇒ (4k) / (k2 + 4) = 1
⇒ k2 - 4k + 4 = 0
⇒ (k - 2)2 = 0
⇒ k - 2 = 0
⇒ k = 2
Therefore, the value of k is 2.
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