Question

find the zeros of the x2 + 3x + 2 quadratic polynomials and verify the relationship​

Answer 1

Answer:

The roots of the given quadratic equation are

x = - 2 or x = - 1

Step-by-step-explanation:

The given quadratic equation is

x² + 3x + 2 = 0.

x² + 3x + 2 = 0

➞ x² + 2x + x + 2 = 0

➞ x ( x + 2 ) + 1 ( x + 2 ) = 0

➞ ( x + 2 ) ( x + 1 ) = 0

➞ x + 2 = 0 or x + 1 = 0

➞ x = - 2 or x = - 1

Now, comparing x² + 3x + 2 = 0 with

ax² + bx + c = 0, we get,

• a = 1

• b = 3

• c = 2

Now,

Sum of zeroes = - b / a

[ ( - 2 ) + ( - 1 ) ] = - 3 / 1

➞ - 2 - 1 = - 3

➞ - 3 = - 3

Also,

Product of zeroes = c / a

[ ( - 2 ) × ( - 1 ) ] = 2 / 1

➞ - 2 × - 1 = 2

➞ 2 = 2

Hence verified!

Additional Information:

1. Quadratic Equation :

An equation having a degree '2' is called quadratic equation.

The general form of quadratic equation is

ax² + bx + c = 0

Where, a, b, c are real numbers and a ≠ 0.

2. Roots of Quadratic Equation:

The roots means nothing but the value of the variable given in the equation.

3. Methods of solving quadratic equation:

There are mainly three methods to solve or find the roots of the quadratic equation.

A) Factorization method

B) Completing square method

C) Formula method

4. Solution of Quadratic Equation by Factorization:

1. Write the given equation in the form ${\sf\:ax^{2} + bx + c = 0}$

2. Find the two linear factors of the ${\sf\:LHS}$ of the equation.

3. Equate each of those linear factor to zero.

4. Solve each equation obtained in 3 and write the roots of the given quadratic equation.

Answer 2

✯✯ QUESTION ✯✯

Find the Zeroes of the ${x}^{2}+3x+2$ Quadratic Polynomials and Verify the Relationship ..

━━━━━━━━━━━━━━━━━━━━

✰✰ ANSWER ✰✰

$\longmapsto\tt{{x}^{2}+3x+2}$

➥By Splitting Middle Term : -

$\longmapsto\tt{{x}^{2}+(2x+1x)+2}$

$\longmapsto\tt{{x}^{2}+2x+1x+2}$

$\longmapsto\tt{x(x+2)+1(x+2}$

$\longmapsto\tt{(x+1)(x+2)}$

Now ,

• x = -1
• x = -2

☛So , -1 and -2 are the zeroes of polynomial x²+3x+2...

➜Here : -

• a = 1
• b = 3
• c = 2

★Sum of Zeroes : -

$\longmapsto\tt{\alpha+\beta=\dfrac{-b}{a}}$

$\longmapsto\tt{-1+(-2)=\dfrac{(-3)}{1}}$

$\longmapsto\tt{-1-2=-3}$

$\longmapsto\tt{-3=-3}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{L.H.S}\orange{=}\purple{R.H.S}}}$

_______________________

★Product of Zeroes : -

$\longmapsto\tt{\alpha\beta=\dfrac{c}{a}}$

$\longmapsto\tt{-1\times{-2}=\dfrac{2}{1}}$

$\longmapsto\tt{2=2}$

$\orange\longmapsto\:\large\underline{\boxed{\bf\purple{L.H.S}\pink{=}\red{R.H.S}}}$

✺ HENCE VERIFIED ✺