Question

find the zeros of the followning quadratic polynomials and verify the relation between the zeros and the coefficients t^2+15​

Answer 1

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• f(x) = t² - 15

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• The zeroes of the given polynomial and also find the relationship between the zeroes and coefficients.

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

We need to use the given identity for solution.

⟶ (a + b)(a - b) = a² - b²

Given that,

⟶ t² - 15 = 0

⟶ t² - (√15)² = 0

⟶ ( t + √15) ( t - √15) = 0

Hence,

⟶ t = -√15

⟶ t = √15

Let α = √15

and β = -√15

________________________________________________

Verification :-

We know,

α + β = - b/a

αβ = c/a

sum of zeroes = 0

⟶ α + β = - b/a

⟶ √15 + (-√15) = 0

L.H.S = R.H.S

Again,

Product of zeroes = -15

αβ = c/a

⟶ √15 × ( -√15) = -15

⟶ -15 = -15

L.H.S = R.H.S

(verified)