Question

Determine the value of k for wch the quadratic equation 4x²-3kx + 1=0 has equal roots.

Answer 1

Here is your answer

Answer 2

Solution :

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Given :

4x² - 3kx + 1= 0 has equal roots.

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To find :

Value of k

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We know that,

The equation  4x² - 3kx + 1= 0,

is in the form ax² + bx + c = 0 ,.

Hence, it is a quadratic equation,.

If a quadratic equation has equal roots, their discriminant is 0,.

⇒ b² - 4ac = 0 (a = 4 , b = -3k , c = 1)

⇒ (-3k)² - 4(4)(1) = 0

⇒ 9k² - 16 = 0

⇒ 9k² = 16

⇒ $k^2 = \frac{16}{9}$

⇒ $k = \sqrt{ \frac{16}{9} }$

⇒ $k = \sqrt{ \frac{(4)^2}{(3)^2} }$

⇒ ∴ $k = \frac{4}{3} (or) k = - \frac{4}{3}$

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