Find the quadratic polynomial the sum and product of its zeros are -1 by (means ÷ ) 4 & 1 by ( means ÷ ) 3
Sum of class 10th
Don't give wrong answer please
and one request is there please solve this question step by step with explanation
Answers
Answer:-
According to the Question
It is given that ,
- Sum of zeros = -1/4
- Product of zeros = 1/3
We have to calculate the quadratic polynomial .
As we know that quadratic polynomial when the sum and product of its zeros are given by
- f(x) = x² -(sum of zeros)x + product of zeros
Substitute the value we get
→ f(x) = x² -(-1/4)x + 1/3
→ f(x) = x² + (1/4)x + 1/3
So, the required quadratic polynomial is
- f(x) = x² + (1/4)x + 1/3
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Extra Information !!
• (a + b)² = a² + b² +2ab
• ( a - b )² = a² + b² -2ab
• ( a² - b² ) = ( a - b ) ( a + b )
• ( a +b +c)² = (a² + b² + c²) + 2(ab + bc +ca)
• (a + b)³ = a³ + b³ + 3ab(a+b)
• (a-b)³ = a³ - b³ -3ab(a-b)
• ( a³ + b³) = (a+b) (a²-ab +b²)
• (a³ - b³) = (a -b) (a² + ab + b²)
Given :-
Sum = -1/4
Product = 1/3
To Find :-
Quadratic polynomial
Solution :-
Standard form of a quardatic polynomial = x² - (α + β)x + αβ
=> x² - (-1/4)x + 1/3
=> x² + 1/4x + 1/12
Hence
Required quadratic polynomial = x² + 1/4x + 1/12