Question

Find the value of k for the followiny equation so that it has two ano equal roots. 5 x 2+ 2K x t 20= 0.​

Answer 1

Given:-

• 5x² + 2kx + 20 = 0 has equal roots

To find:-

• Value of k

Answer:-

It is given that, the quadratic equation has equal roots.

We know that, for a quadratic equation to have equal roots, it's Discriminant, D = b² - 4ac = 0

On comparing 5x² + 2kx + 20 = 0, with the standard form, that is, ax² + bx + c = 0, we get,

• a = 5
• b = 2k
• c = 20

So,

D = 0

→ b² - 4ac = 0

→ (2k)² - (4 * 5 * 20) = 0

→ 4k² - 400 = 0

→ 4k² = 400

→ k² = 100

→ k = ±10 Ans

Extra Knowledge:-

Nature of roots:

• D = 0 ------- Real and equal
• D > 0 and a perfect square ----- Real, unequal and rational
• D > 0 and not a perfect square ------ Real, unequal and irrational
• D < 0 ------- Unequal and imaginary