Question

For what values of k, the equation 9x2+6kx+4=0 has equal roots?

Answer 1

Answer:

k = 2

Step-by-step explanation:

If equation has equal roots then,,

Discriminant (D) = 0

D = b² - 4ac = 0

==: 9x² + 6kx + 4 = 0

a = 9 , b = 6k , c = 4

D = 36k² - 144 = 0

(6k)² - (12)² = 0

(6k - 12) (6k + 12) = 0

k = 2

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Answer 2

Given:

A quadratic equation 9x² + 6kx + 4 = 0 has equal roots.

To Find:

The value of k such that the equation has equal roots is?

Solution:

The given problem can be solved using the concepts of quadratic equations.    

1. The given quadratic equation is 9x² + 6kx + 4 = 0  

2. For an equation to have equal roots the value of the discriminant is 0,  

=> The discriminant of a quadratic equation ax² + b x + c = 0 is given by the formula,  

=> Discriminant ( D ) = $\sqrt{b^2-4ac}$.  

=> For equal roots D = 0.  

3. Substitute the values in the above formula,  

=>  D = 0,  

=> √[(6k)² - 4(9)(4)] = 0,

=> 36k² -144 = 0,

=> 36k² = 144,

=> k² = 144/36,

=> k² = 4,

=> k = ± 2.

Therefore, the values of k are +2 and -2.