Question

Determine the nature of roots of the following quadratic equations from their discriminant. m + 2m + 9 =

0​

Answer 1

C O R R E C T Q U E S T I O N :

Determine the nature of roots of the following quadratic equations from their discriminant. m² + 2m + 9 = 0

S O L U T I O N :

Given,

• Quadratic polynomial, m² + 2m + 9 = 0.

To Find,

• The nature of roots.

Explanation,

Given, quadratic polynomial, m² + 2m + 9 = 0.

On comparing with, ax² + bx + c = 0 , We get,

=> a = 1 , b = 2 , c = 9

We know,

Discriminate = b² - 4ac

[ Put the values ]

=> (2)² - 4 × 1 × 9

=> 4 - 36

=> -32

.°. D < 0

Therefore,

The roots are not real and unequal.

Answer 2

ɢɪᴠᴇɴ

• Correct Quadratic Equation
• → m² + 2m + 9 = 0

⠀

ᴛᴏ ꜰɪɴᴅ

• Nature of roots .

⠀

ꜱᴏʟᴜᴛɪᴏɴ

• We have a quadratic equation given in the question.

⠀

Let's find the Discriminant

⠀

$\large\bf{\boxed{\bigg\lgroup{D = b^2 - 4ac}{\bigg\rgroup}}}$

⠀

Here,

• a = 1
• b = 2
• c = 9

⠀

Putting the values in formula

$\tt:\implies\: \: \: \: \: \: \: \: {D = (2)^2 - 4(1)(9)}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {D = 4 - 36}$

⠀

$\bf:\implies\: \: \: \: \: \: \: \: {D = -32}$

⠀

Here, we get that

⠀⠀⠀⠀⠀⠀⠀❍ D < 0

⠀

Hence,

• The roots of the given Quadratic Equation are not real and unequal.

━━━━━━━━━━━━━━━━━━━━━━