Question

find the value of discriminant

Answer 1

Step-by-step explanation:

In order to find the discriminant of any quadratic equation, we can apply formula for discriminant which is :-

⇝ D = b² - 4ac

Here :-

• D = Discriminant
• a = coefficient of x²
• b = coefficient of x
• c = constant term

Now let's solve the problems !

(1.) x² + 7x - 1 = 0

⇝ D = b² - 4ac

⇝ D = (7)² - 4 (1) (-1)

⇝ D = 49 + 4

⇝ D = 63

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(2.) √2 x² + 4x + 2√2 = 0

⇝ D = b² - 4 a c

⇝ D = (4)² - (4) (√2) (2√2)

⇝ D = 16 - 4 (2 × 2)

⇝ D = 16 - 4 (4)

⇝ D = 16 - 16

⇝ D = 0

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(3.) 2m² -5m + 10 = 0

⇝ D = b² - 4 ac

⇝ D = (-5)² - 4 (2)(10)

⇝ D = 25 - 80

⇝ D = - 55

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(4.) m² + 2m + 9 = 0

⇝ D = b² - 4ac

⇝ D = (2)² - 4 (1) (9)

⇝ D = 4 - 36

⇝ D = 32

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(5.) 2x² - 4x - 3 = 0

⇝ D = b² - 4ac

⇝ D = (-4)² - 4(2)(-3)

⇝ D = 16 + 24

⇝ D = 40

More :-

• In case there is no x or x² don't be confused, x refers to the variable present in the question. Just remember about the constant term, coefficient of variable and coefficient of square of variable.

• If value of discriminant is less than 0, it means that no real value of x can satisfy the equation.

• If value of discriminant is greater than 0, it means that two distinct (or different) values of x can satisfy the given equation.

• If value of discriminant is 0, it means that both the roots of given quadratic equation will be equal.