Question

form a quadratic polynomial whose sum of zero and product of zero are 2 and -5​

Answer 1

Answer:

Here you go!

Step-by-step explanation:

Sum of roots= 2

Product of roots= -5

Formula to find quadratic polynomial

p(x)= k[x²- (Sum of roots)x + (Product of roots)]

     = k[x²-2x+5]

p(x)= x²-2x+5

This is the quadratic polynomial required.

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Answer 2

$\huge\mathcal{\fcolorbox{cyan}{black}{\pink{ANSWER}}}$

Given,

$sum \: of \: zero \: \: \alpha + \beta = 2$

$product \: of \: zero \: \: \alpha \beta = - 5$

Now the equation is :

${x}^{2} - (\alpha + \beta) x + \alpha \beta = 0 \\ \implies \: {x}^{2} - 2x - 5 = 0$

So the polynomial is

$f(x) = {x}^{2} - 2x - 5$