Find the value of m if one zero of the polynomial (m sqaure + 4) * xsquare +65x +4m is the reciprocal of the other.
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If your query is to find the value of m if one zero of the polynomial
(m2+4)x2 + 65x + 4m is reciprocal of the other
If one zero is reciprocal of the other. Let the zeroes of the given polynomial is α and 1/α.
Product of the zeroes =α × 1/α =1 ⇒ 4m / (m2 +4) = 1
⇒ 4m = (m2 + 4) ⇒ (m2 - 4m +4 ) = 0 ⇒ (m - 2)2 = 0 ∴ m = 2
(m2+4)x2 + 65x + 4m is reciprocal of the other
If one zero is reciprocal of the other. Let the zeroes of the given polynomial is α and 1/α.
Product of the zeroes =α × 1/α =1 ⇒ 4m / (m2 +4) = 1
⇒ 4m = (m2 + 4) ⇒ (m2 - 4m +4 ) = 0 ⇒ (m - 2)2 = 0 ∴ m = 2
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