Question

find the nature of the roots of the equation 2x²+6x+7 =0





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Answer 1

Step-by-step explanation:

the formula is root of b^2-4ac

√6^2-4(2)(7)

√36-56=✓-20

as the discriminant is less than 0 there no real roots

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Answer 2

Given:- A quadratic equation is Given to us , which is 2x² + 6x + 7 = 0 .

To Find:- The nature of roots .

Answer:- Given quadratic equation to us is , 2x² + 6x + 7 = 0 . With respect to Standard form ax² + bx + c = 0 ,

• a = 2
• b = 6
• c = 7 .

Nature of roots is determined by Discriminant .

which is equal to b² - 4ac .

Conditions :

• b² - 4ac > 0 , Roots are real
• b² - 4ac = 0 , Roots are equal.
• b² - 4ac < 0 , Roots are complex.

Here ,

=> Discriminant = b² - 4ac

=> Discriminant = 6² - 4 × 2 × 7

=> Discriminant = 36 - 56.

=> Discriminant = (-20)

Since the Discriminant is less than 0 , Hence the roots are complex .

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