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