Question

Find a quadratic polynomial whose sum and product of zeroes are 5 and 2 respectively.
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Answer 1

Step-by-step explanation:

Find a quadratic polynomial whose sum and product of zeroes are 5 and 2 respectively.

answer :::::: k [x²- 8x +5]

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Answer 2

Let the quadratic polynomial be ax²+bx+c and its zeros be α and β.

We have $\displaystyle \tt(α+β) = 5 = \frac{ - b}{a} \: and \: \alpha \beta = 2 = \frac{c}{a}$

If we take a=1, then b=5 and c=2

So, one quadratic polynomial which fits the given conditions is x²+5x+2.

Similarly, we can take 'a' to be any real number.

Let us take it is k.

This gives $\displaystyle \tt \frac{ - b}{k} = 5$

or b=5k and $\displaystyle \tt \frac{ c}{k} = 2$ or c=2k.

Substituting the values of a,b and c,

We get the polynomial is kx²+5x+2k.

$\:$

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