Question

Find the value of k, if the roots of the quadratic equation 2x2 – 6x + k =0

are real and equal​

Answer 1

Answer:

k = 9/2

Step-by-step explanation:

For solving this question, let's understand the concept.

Concept used:

When D = 0 ⇒ Roots are real and equal

Solution:

  D = 0

⇒ b² - 4ac = 0

⇒ b² = 4ac

In the given Quadratic equation,

• a = 2
• b = -6
• c = k

  b² = 4ac

➝ (-6)² = 4(2)(k)

➝ 36 = 8k

➝ k = 36 ÷ 8

∴ k = 9/2

Verification:

Substitute the value of k in the given equation to check whether the quadratic equation has real roots or not.

2x² - 6x + 9/2 = 0

➟ 4x² - 12x + 9 = 0

➟ 4x² - 6x - 6x + 9 = 0

➟ 2x(2x - 3) - 3(2x - 2) = 0

➟ (2x - 2) (2x - 2) = 0

Here, we can observe that roots are 1 and 1 and so they are real and equal.

KNOW MORE:

• When D > 0 → roots are real and unequal
• When D < 0 → roots are imaginary