Question

The zero of the following polynomial 3x+15x+12x​

Answer 1

Answer:

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,

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

$$\rule{150}{1}$$

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!]

Answer 2

Correct question:

The zeroes of the following polynomial 3x²+15x+12

Solution:

Given:

The polynomial 3x²+15x+12

To find:

The zeroes of the given polynomial

Calculation:

The zeroes of the polymial can be found by using factorisation method

=> 3x²+15x+12 = 0

    3x²+12x+3x+12 = 0

    3x(x+4) + 3(x+4) = 0

    (3x+3)(x+4) =0

Case 1:

 => 3x+3 = 0

      3x = -3

      x = -1

Case 2:

 => x+4 = 0

      x = -4

The zeroes of the polynomial 3x²+15x+12 are -1, -4