Question

a quadratic polynomial with sum and product of its zeros as 8 and -9 respectively is:
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Answer 1

Step-by-step explanation:

$we \: know.....formula \: of \: quadratic \: equation \: \\ {x}^{2} - ( \alpha + \beta )x + ( \beta . \alpha ) \\ where \: \alpha and \: \beta \: are \: zeroes.... \\ \\ here \: the \: equation \: becomes...... \\ {x}^{2} - 8x - 9$

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Answer 2

Let the zeros of the required polynomial be m and n

According to the question,

★Sum of zeros:

m + n =8

★Product of zeros:

mn= -9

We know that,

Every polynomial is of the form:

k[x²-(sum of zeros)x+product of zeros]

→k[x²-8x-9]

If k=1,

p(x)=x²-8x-9

• Hence,the quadratic polynomial is x²-8x-9