Question

find the zeroes of the quadratic polynomial 3x²-12x+12 and verify the relationship between the zeroes and the coeffcients.​

Answer 1

Step-by-step explanation:

Zeroes of polynomial = -1 & -4

\rule{200}{1}

Given :- Polynomial:-

☛ 3x² + 15x + 12 = 0

Let the zeroes be α & β

⇒ 3x² + 15x + 12 = 0

⇒ 3x² + 3x + 12x + 12 = 0

⇒ 3x(x + 1) + 12(x + 1) = 0

⇒ (x + 1)(3x + 12) = 0

⇒ (x + 1)[3 (x + 4)] = 0

⇒ x = -1 or x + 4 = 0

↠ x = -1 |or| x = -4

∴ α = -1

∴ β = -4

Therefore,

\therefore\underline{\textsf{Zeroes of polynomial = {\textbf{-1 \& -4 }}}}∴

Zeroes of polynomial = -1 & -4

\rule{150}{1}

Here,

a = 3

b = 15

c = 12

Verifying the relationship between zeroes & coefficients.

Relationship 1:-

☛ Sum of zeroes = -b/a

↠ (α + β) = -b/a

↠ - 1 + (-4) = -15/3

↠ -1 - 4 = -5

↠ -5 = -5 [Verified!]

Relationship 2:-

☛ Product of zeroes = c/a

↠ αβ = 12/3

↠ (-1) × (-4) = 4

↠ 4 = 4 [Verified!]