Question

For what value of k the quadratic equation 9x2 +8kx+16=0 has equal roots

Answer 1

Quadratic equations have equal roots when D = $b^{2}$ - 4*a*c = 0

here a= 9, b=8k and c = 16

0 = $(8k)^{2}$ - 4*9*16
⇒ 0 = 64$k^{2}$ - 576
⇒ 0 = [tex]k^{2} = 9
⇒ k = 3

Therefore for k = 3 the quadratic equation has equal roots.

Answer 2

Given:

A quadratic equation 9x² + 8kx + 16 = 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 + 8kx + 16 = 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,  

=> √[(8k)² - 4(16)(9)] = 0,

=> 64k² -576 = 0,

=> k² = 576/64,

=> k² = 72/8 = 9,

=> k² = 9,

=> k = +3 (OR) k = -3.

Therefore, the values of k are +3 and -3.