Question

Find the least positive value of k for which the x2+Kx+16=0 has real roots

Answer 1

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.

Answer 2

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.