find the quadratic polynomial whose sum and the product of the zeroes are respectively 4 and 3
Answers
Answer :
x² - 4x + 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) = 4
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 - 4x + 3 ] , k ≠ 0
If k = 1 , then the quadratic polynomial will be : x² - 4x + 3 .
Hence ,
Required quadratic polynomial is :
x² - 4x + 3
Answer:
bcoz it is false
Step-by-step explanation:
find the quadratic polynomial whose sum and the product of the zeroes are respectively 4 and 3