Question

the sum and the product of the zeros of a quadratic polynomial are -1/2 and 1/2, then the polynomial is?

Answer 1

Given
sum of zeroes (α + β) = −(1/2)
Product of zeroes (αβ) = 1/2


Recall that the quadratric polynomial with zeroes α, β is given by x2 − (α + β)x + (αβ) = x2 − [−(1/2)]x + (1/2) = x2 +(1/2)x +1/2

Answer 2

Heya!
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♦Given that :
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⭐Sum of Zeroes => -1/2

⭐Product of Zeroes => 1/2

⭐To find => p ( x )


➰Here we can use the formula,

➡ P ( x ) = x² - sx + p


✔Putting in values we have ,
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P ( x ) = x² + 1/2 x + 1/2 = 0


Further taking LCM ,


$x {}^{2} + \frac{1}{2} x + \frac{1}{2} = 0 \\ \\ \\ = > \frac{2x {}^{2} + x + 1}{2} = 0 \\ \\ p(x) = > > 2x {}^{2} + x + 1 = 0$
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