Find the quadratic polynomial, the sum of whose zeros is -5 and their product is 6
Answers
Answer:
x² + 5x + 6
Step-by-step explanation:
Given:- Sum of roots = - 5 and product of roots = 6.
To Find:- The quadratic polynomial which holds the conditions specified.
Solution:-
A quadratic polynomial is a type of polynomial equation in which the highest degree of any variable is 2. Example - x²+6x+9.
We know that, if m and n are roots of a quadratic equation ax² + bx + c = 0, then the quadratic equation becomes
x² - (m + n)x + mn = 0 ------ ( 1 )
where m + n = sum of roots and mn = product of roots.
Acc. to the question, sum of zeroes = -5 and product of zeroes = 6.
Substituting the given values in equation ( 1 ), we get
x² - (-5)x + 6 = 0
⇒ x²+5x+6 = 0
Therefore, the quadratic polynomial is x² + 5x + 6.
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