Find quadratic polynomial for each of the following pairs of values where the first value stands for sum of zeroes and the second value stands for product of zeroes.
1) 3, 1
2) -2, 4
3) 0, 4
4) √2, 1/5
5) -1/3, 1
6) 1/2, -4
7) 1/3, -1/3
8) -√3, 2
Formation of quadratic polynomial when sum and product of the zeroes are given :
x2 - (sum of the roots)x + product of the roots
1. Answer :
3, 1
sum of zeroes = 3, product of zeroes = 1
Quadratic polynomial :
x2 - 3x + 1
2. Answer :
-2, 4
sum of zeroes = -2, product of zeroes = 4
Quadratic polynomial :
x2 + 2x + 4
3. Answer :
0, 4
sum of zeroes = 0, product of zeroes = 4
Quadratic polynomial :
x2 + 4
4. Answer :
√2, 1/5
sum of zeroes = √2, product of zeroes = 1/5
Quadratic polynomial :
x2 - √2x + (1/5)
5. Answer :
-1/3, 1
sum of zeroes = -1/3, product of zeroes = 1
Quadratic polynomial :
x2 + x/3 + 1
6. Answer :
1/2, -4
sum of zeroes = 1/2, product of zeroes = -4
Quadratic polynomial :
x2 - x/2 - 4
7. Answer :
1/3, -1/3
sum of zeroes = 1/3, product of zeroes = -1/3
Quadratic polynomial :
x2 - x/3 - 1/3
8 Answer :
-√3, 2
sum of zeroes = -√3, product of zeroes = 2
Quadratic polynomial :
x2 + √3x + 2
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