Question

Find the value of m if the zero of the polynomial (m2 + 4) x2+ 63x+ 4mis reciprocal of the other zero.

Answer 1

Let α,β are the zeros of (m²+4)x²+63x+4m=0 . Then α=1/β.
From the relations of roots and coeficients, α+β=-63/(m²+4) and α×β =4m/(m²+4).
∴,1/β×β=4m/(m²+4)
or, 4m/(m²+4)=1
or, 4m=m²+4
or, m²-4m+4=0
or, (m-2)²=0
or, m=2,2

Answer 2

Concept

Zeros of the polynomial are those values of x for which the value of polynomial is zero. We know that the multiplication of the zeros is equal to the ratio of the coefficient of the constant term and the first term. And the sum of the zeros is equal to the negative of the ratio of the coefficient of the second term to the first term.

Given

The given polynomial is

$(m^{2} + 4) x^{2} +63x +4m$

One of the zero is reciprocal of the other zero.

Find

We are asked to calculate the value of m.

Solution

Let the two zeros are s and t. Therefore,

s=1/t

Since we know that, $s + t = -63/(m^{2}+4)$ and $st = 4m/ (m^{2}+4)$

Hence,

$s* 1/s = 4m/ (m^{2}+4)\\1 = 4m/ (m^{2}+4)\\m^{2}-4m+4=0\\m= 2, 2$

Hence the value of m is 2.

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