Question

for what value of k does the equation 9x^2+3kx+4=0 has equal roots

Answer 1

Here,
a=9
b=3k
c=4
b^2-4ac=0 (Since the roots are supposed to be equal)
=>{3k}^2-4(9)(4)=0
=>9k^2-144=0
=>9k^2=144
=>k^2=144/9=16
Hence k=4 or -4.

Answer 2

Given:

A quadratic equation 9x² + 3kx + 4 = 0 has equal roots.

To Find:

The value of k such that it satisfies the given condition is?

Solution:

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

1. The given quadratic equation is   9x² + 3kx + 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,

=> $\sqrt{(3k)^2-4*9*4}$ = 0,

=> 9k² - 144 = 0,

=> 9k² = 144,

=> k² = 144/9,

=> k² = 16.

=> k = +4, -4.

Therefore, the values of k are -4, and +4.