Find the least positive value of k for which the x2+Kx+16=0 has real roots
Answers
Solution.......
x2 + kx + 16 = 0
D is equal to or greater than 0
b2 - 4ac is equal to or greater than 0
k2 - 64 = > 0
k2 = > 64
k = > 8
k = 8
The least positive integer value for k is 8.
Given,
The quadratic equation x²+kx+16 is given and the roots of the equation are real.
To find,
We have to find the least positive value of k for the quadratic equation x²+kx+16.
Solution,
The least possible value of k for quadratic equation x²+kx+16 is 8.
We can simply find the least positive value of k for the quadratic equation x²+kx+16 by using the discriminant formula.
D = b²-4ac
D = K² -4(1)(16)
D = K² -64
If the roots of the quadratic equation are real then D must be greater than 0 i.e. D>0
K² -64 >0
K² > 64
K >8
Hence, the least positive value of k for which the x2+Kx+16=0 has real roots is 8.