Question

11. Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficients of the polynomial
${y}^{2} + \frac{3}{2} \sqrt{5} \ y - 5$
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Answer 1

2y^2+3√5y-10=0

2y^2+4√5y-√5y-10=0

2y(y+2√5)-√5(y+2√5)=0

(y+2√5) (2y-√5)=0

y = -2√5 or y = √5/2

Comparing  the equation y^2+3/2√5y-5 it with general form ax^2+bx+c=0

a = 1, b = 3/2√5 and c = -5

Relation Between Zeroes and Coefficients are:

α + β = -b/a where α = -2√5 and β = √5/2

αβ = c/a

LHS = α + β = -2√5 + √5/2 = -3√5/2

RHS = -b/a = -3/2√5/1 = 3/2√5

LHS = RHS

αβ = c/a, where α = -2√5 and β = √5/2

LHS = αβ = -2√5 *√5/2 = -5

RHS = c/a = -5/1 = -5

LHS = RHS

Hence, Verified