Question

Find the zeros of the quadratic polynomial and verify the relation between zeros and coefficients 3x2+15x+12

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

$\mathtt{ \huge{ \fbox{Solution :)}}}$

Given ,

The polynomial is 3x² + 15x + 12

Thus ,

➡3x² + 15x + 12 = 0

➡3x² + 3x + 12x + 12 = 0

➡3x(x + 1) + 12(x + 1) = 0

➡(3x + 12) (x + 1) = 0

➡x = -4 or x = - 1

Hence , the roots of quadratic equation is -4 and -1

$\mathtt{ \huge{ \fbox{ Verification :)}}}$

We know that ,

The relationship between zeroes and coefficient of quadratic equation is given by

$\large \mathtt{ \fbox{Sum \: of \: roots = - \frac{b}{a} }}$

Thus ,

(-4) + (-1) = -15/3

-5 = -5

And

$\large \mathtt{ \fbox{Product \: o f \: roots = \frac{c}{a} }}$

Thus ,

(-4) × (-1) = 12/3

4 = 4

Hence verified

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