Question

identity the nature of root of x^2-3x+4root2=0​

Answer 1

1. Step-by-step explanation:

I hope. it will. help. you

Answer 2

Answer:

The roots are imaginary, there are no real roots.

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Step-by-step explanation:

We've been given a quadratic equation, and we're asked to find the nature of the roots.

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The equation is x² - 3x + 4√2​, where;

• a = co-efficient of x² = 1

• b = co-efficient of x = -3

• c = constant term = 4√2 ‎

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We know that the nature of the roots of a quadratic equation is given by its discriminant (D).‎‎

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Discriminant (D) = b² - 4ac‎‎

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1) If D > 0

• Nature of roots: Roots are real, both the roots are distinct. (Unequal)‎‎

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2) If D = 0

• Nature of the roots: Roots are real, both the roots are equal.‎‎

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3) If D < 0

• Nature of the roots: Roots are imaginary, there are no real roots.‎

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For the quadratic equation x² - 3x + 4√2​;

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‎⇒ Discriminant (D) = b² - 4ac

⇒ Discriminant (D) = (-3)² - 4(1)(4√2)

⇒ Discriminant (D) = 9 - 16√2

⇒ Discriminant (D) = 9 - 16(1.414)

⇒ Discriminant (D) = 9 - 22.624

⇒ Discriminant (D) = -13.6274 (approx)

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Here, D = -13.6274, meaning D < 0.

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∴ The nature of the roots are imaginary, there are no real roots.