Question

Find The quadratic polynomial whoes zeroes are 3+root5 and 3-root5

Answer 1

Hello user

Let's assume the quadratic polynomial to be ax^2 + bcoz + c

So, we can have..

ax^2 + bcoz + c = (x - 3 - 5^1/2)(x - 3 + 5^1/2)

ax^2 + bcoz + c = (x-3)^2 - 5

ax^2 + bcoz + c = x^2 + 9 - 6x - 5

ax^2 + bcoz + c = x^2 - 6x + 4

Since, a = 1 here

So, the quadratic polynomial will be... (x^2 - 6x + 4)

Hope it works

Answer 2

Let the polynomial be ax^2 + bx + c.

(i)

We know that sum of zeroes = -b/a

⇒ 3 + √5 + 3 - √5 = -b/a

⇒ 6 = -b/1

⇒ -b = 6

⇒ b = -6

(ii)

Product of zeroes = c/a

⇒ (3 + √5)(3 - √5) = c/a

⇒ (3)^2 - (√5)^2 = c/1

⇒ 9 - 5 = c

⇒ c = 4.

Therefore, the required quadratic polynomial = ax^2 + bx + c

⇒ x^2 - 6x + 4.

Hope this helps!