Question

Find a quadratic polynomial whose sum of zeros and product of zeros are -5 and -4 ?


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Answer 1

Answer:

The quadratic polynomial is x²+9x+20

Explanation:

Let m and n be the zeros of the required quadratic polynomial

Implies,

$\mathsf{m= -5 and n= -4}$

★Any quadratic polynomial would be of the form:

$\mathsf{x {}^{2} - (sum \: of \: zeros)x + product \: of \: zeros }$

Here,

★Sum of Zeros

m + n

= -5 + (-4)

= -9

★Product of zeros

mn = (-5)(-4) = 20

Now,

The polynomial would be:

$\mathsf{x {}^{2} - (m + n)x + mn } \\ \\ \implies \: \mathsf{x {}^{2} - ( - 9)x + 20 } \\ \\ \implies \: \underline{\huge{\boxed{ \sf{x {}^{2} + 9x + 20}}}}$

Answer 2

Step-by-step explanation:

Hi,

Sum of zeroes = (-5)

And,

Product of zeroes = -4

Therefore,

Required quadratic polynomial = x² - ( sum of zeroes ) x + Product of zeroes.

=> X² - (-5)x + (-4)

=> x² + 5x - 4

Hope it will help you :)