Question

Find the values of k for which the roots are real and equal kx² – 2√5 x + 4 = 0

Answer 1

$\large\bf\underline {To \: find:-}$

• we need to find the Value of k.

$\large\bf\underline{Given:-}$

• kx² - 2√5x + 4 has two real and equal roots

$\huge\bf\underline{Solution:-}$

If the equation has two real and equal roots then , Discriminant = 0

$\bf \star \: {b}^{2} - 4ac = 0$

☘ Equation :- kx² - 2√5x + 4

where,

• a = k
• b = - 2√5
• c = 4

• b² - 4ac = 0

➛ (-2√5)² - 4 × k × 4 = 0

➛ 4 × 5 - 16k = 0

➛ 20 - 16k = 0

➛ - 16k = -20

➛ k = 20/16

➛ k = 5/4

Hence,

• ❥ Value of k is 5/4

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Answer 2

◆ kx²– 2√5 x + 4 = 0

★ Here, a = k, b = – 2√5 x , c = 4

★ Given roots are equal,

◆ D = b^2 – 4ac = 0

________________________

Solution :-

⇒ (-2√5)² - 4 × k × 4 = 0

⇒ 4 × 5 - 16k = 0

⇒ 20 - 16k = 0

⇒ - 16k = -20

⇒ k = 20/16

⇒ k = 5/4

Hence :-

The required value of K = 5/4

$\sf$