(x+ 4)² - 8x = 0. State whether the following quadratic equation has two distinct real roots

Solution:

Given, the equation is (x + 4)² - 8x = 0

We have to determine if the equation has two distinct real roots.

By using algebraic identity,

(a + b)² = a² + 2ab + b²

(x + 4)² = x² + 8x + 16

 x² + 8x + 16 - 8x = 0

 x² + 16 = 0

Discriminant = b² - 4ac

Here, a = 1, b = 0 and c = 16

b² - 4ac = 0 - 4(1)(16)

= 0 - 64

= -64 < 0

We know that a quadratic equation ax² + bx + c = 0 has no real roots when the discriminant of the equation is less than zero.

Therefore, the equation has no real roots.

✦ Try This: Determine the nature of the quadratic equation x² + 2x - 3 = 0

Given, the equation is x² + 2x - 3 = 0

We have to determine if the equation has two distinct real roots.

Discriminant = b² - 4ac

Here, a = 1, b = 2 and c = -3

b² - 4ac = (2)² - 4(1)(-3)

= 4 + 12

= 16 > 0

We know that a quadratic equation ax² + bx + c = 0 has 2 distinct real roots when the discriminant of the equation is greater than zero.

Therefore, the equation has 2 distinct real roots

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4

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NCERT Exemplar Class 10 Maths Exercise 4.2 Problem 1 (v)

(x+ 4)² - 8x = 0. State whether the following quadratic equation has two distinct real roots

Summary:

The equation (x+ 4)² - 8x = 0 has no real roots.

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