Question

X2-4x+k=0 and x2+kx-4=0 where k is a real no. Find the value of k

Answer 1

x2-4x+k=0
D=b2-4ac
(-4)2-4×1×k=0
16-4k=0
-4k=-16
k=4

And

x2+kx-4

(k)2-4×1×-4=0
k2+16=0
k2=-16
k=not possible or imaginary no.

Answer 2

Answer:

3

Step-by-step explanation:

First equation :

x² + kx - 4 = 0

k = the sum of the roots

-4 = the product of the roots

The possible roots that will give a negative product is :

-1 and 4, - 2 and 2, - 4 and 1

Since the sum of the roots is a positive number, we take a combination of roots whose sum is positive.

4 and - 1

Thus k is :

k = - 1 + 4 = 3

Second equation :

x² - 4x + 3 = 0

The roots of this equation is :

-1 and - 3 hence it is a quadratic equation.

∴ The value of k is 3