form a quadratic polynomial whose sum of zeros is-4 and product of zeros is 8
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Answers
Answer :
x² + 4x + 8
Note :
★ The possible values of the variable for which the polynomial becomes zero are called its zeros .
★ A quadratic polynomial can have atmost two zeros .
★ The general form of a quadratic polynomial is given as ; ax² + bx + c .
★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;
• Sum of zeros , (α + ß) = -b/a
• Product of zeros , (αß) = c/a
★ If α and ß are the zeros of a quadratic polynomial , then that quadratic polynomial is given as : k•[ x² - (α + ß)x + αß ] , k ≠ 0.
Solution :
• Given : Sum of zeros = -4
Product of zeros = 8
• To find : The quadratic polynomial
Let α and ß be the zeros of required quadratic polynomial .
Thus ,
=> Sum of zeros = -4
=> α + ß = -4
Also ,
=> Product of zeros = 8
=> αß = 8
Now ,
We know that , ig α and ß are the zeros of a quadratic polynomial , then that quadratic polynomial is given as : k•[ x² - (α + ß)x + αß ] , k ≠ 0.
Thus ,
The required quadratic polynomial will be given as ;
=> k•[ x² - (-4)x + 8 ] , k ≠ 0
=> k•[ x² + 4x + 8 ] , k ≠ 0
If k = 1 , then the quadratic polynomial will be : x² + 4x + 8 .