Question

please help me quick man ​

Answer 1

Question :-

• Find the value of m, if one zero of the Polynomial (m² + 4)x² + 65x + 4m is reciprocal of the other ?

Concept used :-

The sum of the roots of the Equation ax² + bx + c = 0 , is given by = (-b/a)

and ,

→ Product of roots of the Equation is given by = c/a.

Solution :-

Let , Zeros of the Given Polynoimal are ɑ & β.

Since One Zeros is reciprocal of the other .

So,

we can say that :-

→ β = 1/ɑ

Or,

→ ɑ = 1/β

or, we can conclude That,

→ ɑ × β = 1. ------------------ Equation ❶

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Now, Comparing The Given Polynomial (m² + 4)x² + 65x + 4m with ax² + bx + c , we get,

→ a = (m² + 4)

→ b = 65

→ c = 4m .

So,

➼ Product of Zeros = c/a

➼ Product of Zeros = 4m/(m² + 4) ------ Equation ❷

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Putting Equation ❶ = Equation ❷, we get,

☛ 1 = 4m / (m² + 4)

☛ m² + 4 = 4m

☛ m² - 4m + 4 = 0

☛ m² - 2m - 2m + 4 = 0

☛ m(m - 2) -2(m - 2) = 0

☛ (m - 2)(m - 2) = 0

☛ (m - 2)² = 0

Putting Equal to Zero,

☛ m = 2 (Ans.)

Answer 2

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$\huge\tt{PROBLEM:}$

Find the value of m, if one zero of the polynomial (m²+4)x²+65x+4m is reciprocal of the other.

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$\huge\tt{GIVEN:}$

• zero of the polynomial is reciprocal of the other one

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$\huge\tt{TO~FIND:}$

• value of m

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$\huge\tt{SOLUTION:}$

Let the zeros of polynomial be P & Q

as we know, one zero is reciprocal of the other

We can say that

↪p = 1/q

↪q = 1/p

Or,

p × q = 1 ____(EQ.1)

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By comparing the polynomial we get,

➡a = (m²+4)

➡b = 65

➡c = 4 m

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Then,

⏭ Products of zero = c/a

⏭ Products of zero = 4m/(m²+4) _____(EQ.2)

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Now, comparing both equations...

▶1=4m/(m²+4)

▶m² +4 = 4m

▶m²-4m +4 = 0

▶m(m-2)-2(m-2) = 0

▶(m-2)(m-2) = 0

▶(m-2)² = 0

▶m = 2

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