Find a quadratic polynomial whose zeros are –4 and 2.
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Answer:
Quadratic Polynomial is k ( x² + 2x - 8 )
Step-by-step explanation:
Given: Zeroes of quadratic Polynomial are -4 and 2
To find: Quadratic Polynomial
If α and β are zeroes of quadratic polynomial than the quadratic polynomial is given by k ( x² - ( α + β ) x + αβ )
where , ( α + β ) is sum of zeroes and αβ is product of zeroes.
Here, α = - 4 and β = 2
⇒ α + β = -4 + 2 = -2
αβ = -4 × 2 = -8
⇒ Quadratic Polynomial = k ( x² - ( -2 ) x + ( -8 ) )
= k ( x² + 2x - 8 )
Therefore, Quadratic Polynomial is k ( x² + 2x - 8 )
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