Question

the sum and product of the zeros of a quadratic polynomial are - 1 / 2 and -3 respectively . what is the quadratic polynomial.

Answer 1

quadratic polynomial = X^2-X(sum)+product
= X^2+1/2X-3

Answer 2

Step-by-step explanation:

AnswEr:

$\bold{\underline{\sf{\red{\;\;Given:-\;\;}}}}$

Sum of Zeroes = $\sf\dfrac{-1}{\;\;2}$

Product of Zeroes = -3

$:\implies\sf\;Sum \; of \; Zeroes\; = (\alpha + \beta)$

$:\implies\sf\; Product \; of \;Zeroes\; = (\alpha\;\beta)$

$:\implies\sf(\alpha + \beta) = \dfrac{-1}{\;\;2}$

$:\implies\sf\;(\alpha \; \beta) = -3$

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By using the Formula:-

$:\implies\large{\underline{\boxed{\sf{\pink{x^2 - (\alpha + \beta)x + (\alpha\;\beta)}}}}}$

Now, Putting Values:-

$:\implies\sf\;x^2 - \dfrac{-1}{\;\;2} + -3$

$:\implies\large{\underline{\boxed{\sf{\pink{2x^2 - x - 6}}}}}$

Therefore, The Required Polynomial is 2x² - x - 6.

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