Question

3. If the equation 3x2 – kx + 2k = 0 has equal roots, then the value(s) of k is (are)
(a) 6
(b) O only (c) 24 only (d) 0 or 24
​

Answer 1

Answer: The value of k are 0 and 24

Step-by-step explanation:

As we have given the equation in the question that 3x²-kx+2k=0 has equal roots

So we know that, The Descriminant of any quadratic equation is zero which has equal roots.

So, D² = b²-4ac

0= (-k)²-4*3*2k

k²-24k=0

k=24,0

Answer 2

Given

$3x^2-kx + 2k = 0$ has equal roots

To find

Value of $k$

Solution

If the quadratic equation has equal roots then the discriminant is 0.

$a = 3$

$b = -k$

$c = 2k$

So, the discriminant is

$D=b^2-4ac\\\Rightarrow 0=(-k)^2-4\times 3\times2k\\\Rightarrow 0=k^2-24k\\\Rightarrow k(k-24)=0\\\Rightarrow k-24=0\\\Rightarrow k=24$

The value of $k$ is $24$ only.