Question

5m^2+2m+1=0 solve the quadratic equations
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Answer 1

Answer:

D<0

therefore, no roots exist

Answer 2

Answer:

The roots of the given quadratic equation are

$m \: = \frac{ \sqrt{ - 16} }{10} \: \: or \: \: m \: = \frac{ - \sqrt{ - 16} }{10}$

Step-by-step-explanation:

NOTE : Kindly refer to the attachment first.

The given quadratic equation is

5m² + 2m + 1 = 0

Comparing with ax² + bx + c = 0, we get,

a = 5, b = 2, c = 1

Now,

b² - 4ac = ( 2 )² - ( 4 × 5 × 1 )

∴ b² - 4ac = 4 - 20

∴ b² - 4ac = ( - 16 )

Now, by using formula for quadratic equation, we get,

$m \: = \: \frac{ ∓ \: \sqrt{ {b}^{2} - 4ac } }{2a} \: \: ...( \: formula \: ) \\ \\⇒ \: m \: = \frac{ ∓ \sqrt{ - 16} }{2 \times 5} \\ \\ ⇒ \: m = \frac{∓ \sqrt{ - 16} }{10} \\ \\ ∴ \: m \: = \frac{ \sqrt{ - 16} }{10} \: \: or \: \: m \: = \frac{ - \sqrt{ - 16} }{10}$

Ans.: The roots of the given quadratic equation are

$m \: = \frac{ \sqrt{ - 16} }{10} \: \: or \: \: m \: = \frac{ - \sqrt{ - 16} }{10}$

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.