Find a quadratic polynomial with given numbers as the sum and product
of zeroes respectively -2 and -3.
Answers
Answer :
x² + 2x - 3
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 , (α + ß) = -2
Product of zeros , (αß) = -3
• To find : A quadratic polynomial
We know that ,
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.
Thus ,
Required quadratic polynomial will be given as :
=> k•[ x² - (α + ß)x + αß ] , k ≠ 0
=> k•[ x² - (-2)x + (-3) ] , k ≠ 0
=> k•[ x² + 2x - 3 ] , k ≠ 0
If k = 1 , then the quadratic polynomial will be : x² + 2x - 3 .