Math, asked by ItzDazzledBoi, 5 months ago

Find the zeroes of the polynomial f(x) = 4x² + 8x and verify the relationship between the zeroes and its coefficients. ​

Answers

Answered by hkishor60gmailcom
5

F(x)= 4x²+8x

let f(x) be f(0)

f(0)= 4×0²+8×0= 0

please mark it as brainlist answer

Answered by MaIeficent
26

Step-by-step explanation:

Given:-

  • A quadratic polynomial f(x) = 4x² + 8x

To Find:-

  • The zeroes of the polynomial

  • And verify the relationship between the zeroes and coefficients.

Concept used:-

For a quadratic polynomial f(x) = ax² + bx + c

Sum of zeroes = \rm \dfrac{-b}{a}

Product of zeroes = \rm \dfrac{c}{a}

In the given quadratic equation 4x² + 8x

a = 4 , b = 8 and c = 0

Solution:-

f(x) = 4x² + 8x

\sf  \implies4 {x}^{2}   + 8x = 0

By factorization:-

 \sf  \implies4x(x  + 2) = 0

\sf  \implies4x = 0 \:  \:  \: (or) \:  \:  \: x  + 2= 0

\sf  \implies x =  \dfrac{0}{4}  \:  \:  \: (or) \:  \:  \: x = 0 - 2

\sf  \implies x = 0 \:  \:  \: (or) \:  \:  \: x  =  - 2

Therefore, the zeroes are 0 and -2

Now, let us verify the relationship between the zeroes and coefficients.

\sf Sum \: of \: zeroes = 0 + (-2) = -2

\sf  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: =  \dfrac{-b}{a} = \dfrac{ - 8}{4}  = -2

\sf  \therefore Sum \: of \: zeroes =  \dfrac{ - (Coefficient \: of \:  x) }{Coefficient \: of \:   {x}^{2} }

\sf Product \: of \: zeroes = 0 \times -2 = 0

\sf  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  =  \dfrac{c}{a} =  \dfrac{0}{4}  = 0

\sf  \therefore Product \: of \: zeroes =  \dfrac{ Constant\: term}{Coefficient \: of \:   {x}^{2} }

Hence Verified

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