For what value of k does the equation x2 + kx + 9have:
Two distinct real roots
One real root
No real root
4 answers
One real root.
First of all you don't have an equation, you must have meant:
x^2 + kx + 9 = 0
For two distinct real roots, the discriminant b^2 - 4ac > 0
k^2 - 4(1)(9) > 0
k^2 > 36
±k > 6
k > 6 or k < -6
To have 1 root, the discriminant b^2 - 4ac must be zero
k^2 - 4(1)(9) = 0
k^2 = 36
k = ± 6
So what do you think must be the value of b^2 - 4ac to have no real roots ?
x^2 + kx + 9 = 0
For two distinct real roots, the discriminant b^2 - 4ac > 0
k^2 - 4(1)(9) > 0
k^2 > 36
±k > 6
k > 6 or k < -6
To have 1 root, the discriminant b^2 - 4ac must be zero
k^2 - 4(1)(9) = 0
k^2 = 36
k = ± 6
So what do you think must be the value of b^2 - 4ac to have no real roots ?
6 > k > -6 no roots?
yes, I would prefer you last statement to say
-6 < k < 6
I know it is the same thing as your answer, but traditionally let's go
from left to right . Visualize the number line, negatives on the left.
for -10 < x < 10 , I visualize x to be between -10 and + 10
-6 < k < 6
I know it is the same thing as your answer, but traditionally let's go
from left to right . Visualize the number line, negatives on the left.
for -10 < x < 10 , I visualize x to be between -10 and + 10
0 answers