Form a quadratic polynomial, one of whose zero is 2 + root5 and the sum of zeros is 4 - Maths - Polynomials

Question

Form a quadratic polynomial, one of whose zero is 2 + root5 and the
sum of zeros is 4

Varshini · Accepted Answer

Let,
the given zero = α = 2 +√5
let the other zero be = β
given ,
sum of zeroes = 4
α + β = 4
⇒ 2 +√5 +β = 4
⇒ β = 4-(2+√5)
⇒β = 2- √5
the quadratic polynomial whose zeroes are α and β
is:
k[ x² -(α + β)x + αβ ] = 0
⇒ k[x² -{(2+√5)+(2-√5)}x +
(2-√5)(2+√5) ] = 0
⇒ k [ x² - 4x +(4-5) ] = 0
⇒k[ x² - 4x -1] = 0 since (a² -b²) =
(a+b)(a-b)
if k = 1 the required equation is x² - 4x -1 =
0

Form a quadratic polynomial, one of whose zero is 2 + root5 and the sum of zeros is 4.