Question

the smallest value of k for which the equation x^2+kx+9=0 has real roots is​

Answer 1

Answer:

The given quadratic equation is x

2

−kx+9=0, comparing it with ax

2

+bx+c=0

∴ We get, a=1b=−k,c=9

⇒ It is given that roots are real and distinct.

∴ b

2

−4ac>0

⇒ (−k)

2

−4(1)(9)>0

⇒ k

2

−36>0

⇒ k

2

>36

⇒ k>6 or k<−6

∴ We can see values of k given in question are correct.

Answer 2

Step-by-step explanation:

b² - 4ac >= 0 for real roots

k² - 4 × 1× 9 >= 0

k² - 36 >= 0

k² >= 36

k >= 6

so smallest number can be 6