Question

find the value of k they have two real roots and equal roots 5x²-2kx+20=0​

Answer 1

Required Answer:-

Given:

• 5x² - 2kx + 20 = 0.

To find:

• The value of k such that the roots of the given equation are real and equal.

Solution:

We have,

➡ 5x² - 2kx + 20 = 0.

Here,

➡ a (coefficient of x²) = 5

➡ b (coefficient of x) = -2k

➡ c (coefficient of x⁰) = 20

We know that if the roots of a quadratic equation are real and equal then the discriminant is equal to zero. Using this concept, we will solve this problem.

Now,

★ Discriminant Δ = b² - 4ac

So, according to the conditions,

➡ (-2k)² - 4 × 5 × 20 = 0

➡ 4k² - 400 = 0

➡ 4(k² - 100) = 0

➡ k² - 100 = 0

➡ k² = 100

➡ k = √100

➡ k = ±10

Hence, if the values of k are 10 or -10, then the roots of this quadratic equation are equal and real.

Answer:

• The possible values of k are -10 and 10.

Answer 2

Answer:

k are -10 or 10

Step-by-step explanation:

given

5x²-2kx+20=0

a=5,b= -2, c=20

(-2k)²-4×5×20=0

4k²-400=0

4(k²-100)=0

k²-100=0

k=√100

k=±10

Hence, the possible values of k are -10 and 10