Question

Describe the nature of roots of 9x2+7x - 2=0​

Answer 1

Answer:

The roots of this quadratic equation are real and different because D > 0.

Step-by-step explanation:

Answer 2

Required Answer:-

Given Equation:

• 9x² + 7x - 2 = 0

To Find:

• The nature of roots of the given equation.

Solution:

The discriminant of a quadratic equation tells about the nature of roots.

The general form of a quadratic equation is -

→ ax² + bx + c = 0

Discriminant is calculated by using the given formula,

→ D = b² - 4ac

Where,

• a = coefficient of x².
• b = coefficient of x.
• c = constant term.

• If Discriminant is greater than 0, the roots are real and distinct.
• If Discriminant is less than 0, the roots are imaginary and no real roots exist.
• If Discriminant is equal to 0, the roots are real and equal.
• Note: A quadratic equation can have at most two roots.

Given equation,

→ 9x² + 7x - 2 = 0

Here,

→ a = 9

→ b = 7

→ c = -2

So, discriminant will be,

→ D = b² - 4ac

→ D = (7)² - 4 × (9) × (-2)

→ D = 49 + 72

→ D = 121

So, the value of discriminant is 121.

→ As D > 0, the roots are real and distinct.

Answer:

• As discriminant is greater than 0, the roots are real and distinct.

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