Question

find a polynomial whose sum and product of zeroes are -1/2 and -3

Answer 1

Hey there !!!!
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If α and β are the zeroes of the quadratic polynomial p(x)

Then p(x) can be represented as

     p(x) =x²-(α+β)x+αβ

α+β is the sum of roots and αβ is product of the roots.

Now,

   

p(x)= x²-(-1/2 )x+(-3)

p(x)=x²+x/2-3

p(x)=2x²+x-6

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Hope this helped you...............

Answer 2

Hi friend!!

Let à and ß are the zeroes of the polynomial.

Sum of zeroes = -½

à + ß = -½

Product of zeroes = -3

àß = -3

A quadratic polynomial with two zeroes is in the form

k(x² - (à+ß)x + àß)

→ k(x² - (-½)x + (-3))

→ k(x² + x/2 - 3)

Put k = 2

→ 2x²+x-6

Hope it helps...