Question

Find k for which the given quadratic equation 9x² + 3kx + 4 = 0 has distinct roots.

Answer 1

Given quadratic equation is= 9x² + 3kx + 4 = 0

On comparing with standard form of quadratic equation i.e ax² + bx + c =0,a≠0
Here, a = 9 , b= 3k, c= 4

D(discriminant)= b²-4ac
= (3k)² - 4× 9 ×4
= 9k² - 144

Since, roots of given equation are distinct.  D > 0.
9k² - 144 > 0
9(k² - 16) >0
(k² - 16) >0            (9≠0)
k² -4²>0
(k-4) (k+4) >0
[ a² - b² = (a-b)(a+b)]

k > 4 and k< -4

Hence, the value of k is k > 4 and k< -4.

HOPE THIS WILL HELP YOU..

Answer 2

Heya user..!!

Here is ur answer..!!

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Answer:

• k = 4

Step-by-step explanation:

9x²+3kx₊4 = 0

By quadratic formula :

a = 9,  b = 3k , c = 4

b²-4ac =  ( 3k ) ² - 4 ( 9) (4) = 0

            =  9k²- 144 = 0

           = 3 ( 3k² - 48 ) = 0

          = 3 = 0 ,  3k² - 48 = 0

                         3k² = 48

                         k² = 16

                         ∴ k = 4

           = k = 0 or k = 4

       ✔✔ Hence, the required value of k is 4 ✅✅.

• NOTE that please :

• If the equation had real and unequal roots , then :

• b² > 4 ac

• If the equation had imaginary roots then :

• b² < 4 ac

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I Hope this may help u..!!

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