Question

4x2 – 20x + 25 = 0 have


Real and Distinct roots
Real and Equal roots
Real roots
No Real roots

Answer 1

Answer :

The answer is :

Real and Equal roots

Given :

The quadratic equation is :

• 4x² - 20x + 25 = 0

To Find :

• Whether the given equation has :

1. Real and distinct roots or
2. Real and equal roots or
3. Real roots or
4. No real roots

Concept used here :

Discriminant of a quadratic equation (b² - 4ac) :

• If ax² + bx + c is a quadratic equation then b²-4ac is called the discriminant of that equation.
• From the discrimiant we can examine the nature of roots of the given quadratic equation
• Condition of discriminant →

1. If b² - 4ac > 0 , then two distinct and real roots are there
2. If b² - 4ac = 0 , then two real and equal are there
3. if b² - 4ac ≥ 0 , then real roots are there
4. If b² - 4ac < 0 , then no real root is there.

Solution :

Let us consider from the given equation :

a = 4 , b = -20 , and c = 25

Therefore , the discriminant D will be

$\sf{D = {b}^{2} - 4ac} \\ \\ \implies \sf{D = ( - 20) {}^{2} - 4 \times 4 \times 25} \\ \\ \implies \sf{D = 400 - 400} \\ \\ \sf{ \implies D = 0}$

Thus discriminant , b² - 4ac = 0

So the given equation has real and equal roots

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Given Equation,

= 4x² - 20x + 25 = 0

On comparing the equation with ax² + bx + c = 0, we get

Here, a = 4 , b = -20 , and c = 25

We know that,

Discriminant, D = b² - 4ac

D = b² - 4ac

⇒ D = (- 20)² - 4 × 4 × 25

⇒ D = 400 - 400

⇒ D = 0

Since, b² - 4ac = 0

Hence, the given equation has real and equal roots.

More About the Topic :-

For the quadratic equation ax² + bx + c = 0, the expression b² - 4ac is known as discriminant i.e Discriminant, D = b² - 4ac

Nature of roots of a quadratic equation:-

(i). If b² - 4ac > 0, the quadratic equation has two distinct real roots.

(ii). If b² - 4ac = 0, the quadratic equation has two equal real roots.

(iii). If b² - 4ac < 0, the quadratic equation has no real roots.