Question

find a quadratic polynomial for which the sum of the product of zeros are√5 and 3 /4 respectively​

Answer 1

Answer:

Question 2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

(i)1/4 , -1 (ii) √2 , 1/3 (iii) 0, √5 (iv) 1,1 (v) -1/4 ,1/4 (vi) 4,1

Question 2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

(i)1/4 , -1 (ii) √2 , 1/3 (iii) 0, √5 (iv) 1,1 (v) -1/4 ,1/4 (vi) 4,1

(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