Question

2. Find a quadratic polynomial each with the given numbers as the sum and product of its
zeroes respectively.
(1) .-
(iii) 0,5
4
1
(ü) V2.
3
1 1
(iv) 1.1
(v)
(vi) 4.1
4 4​

Answer 1

Step-by-step explanation:

(i)1/4, -1

Now formula of quadratic equation is

x²-(Sum of root)x + (Product of root) = 0

Plug the value in formula we get

x² –(1/4)x -1 = 0

Multiply by 4 to remove denominator we get

4x² - x -4 = 0

(ii) √2 , 1/3

Now formula of quadratic equation is

x²-(Sum of root)x + (Product of root) = 0

Plug the value in formula we get

x² –(√2)x + 1/3 = 0

Multiply by 3 to remove denominator we get

3x² - 3√2 x + 1 = 0

(iii) 0, √5

Now formula of quadratic equation is

x²-(Sum of root)x + (Product of root) = 0

Plug the value in formula we get

x² –(0)x + √5 = 0

simplify it we get

x² + √5 = 0

(iv) 1,1

Now formula of quadratic equation is

x²-(Sum of root)x + (Product of root) = 0

Plug the value in formula we get

x² –(1)x + 1 = 0

simplify it we get

x² - x + 1 = 0

(v) -1/4 ,1/4

Now formula of quadratic equation is

x²-(Sum of root)x + (Product of root) = 0

Plug the value in formula we get

x² –(-1/4)x + 1/4 = 0

multiply by 4 we get

4x² + x + 1 = 0

(vi) 4,1

Now formula of quadratic equation is

x²-(Sum of root)x + (Product of root) = 0

Plug the value in formula we get

x² –(4)x + 1 = 0

x^2 –4x + 1 = 0

Answer 2

Answer:

Alpha Plus beta is equal to minus b by a

alpha beta is equal to c by a

now sum of zeros is alpha + beta and product of zeros is alpha beta put the formula in making quadratic equation ax²+bx+c