find the value of K if the given equation 4x²-3Kx+1=0
Answers
Answer:
-4/3
Step-by-step explanation:
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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
2
=
9
16
⇒ k = \sqrt{ \frac{16}{9} }k=
9
16
⇒ k = \sqrt{ \frac{(4)^2}{(3)^2} }k=
(3)
2
(4)
2
⇒ ∴ k = \frac{4}{3} (or) k = - \frac{4}{3}k=
3
4
(or)k=−
3
4
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Answer:
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