Answer:
k = 12
Step-by-step explanation:
Given:
The equation [tex]Q(x)=2x^2-kx+18[/tex]
To find:
Value of [tex]k = ?[/tex] for which the given equation has one distinct real solution.
Solution:
The given equation is a quadratic equation.
There are always two solutions of a quadratic equation.
For the equation: [tex]ax^{2} +bx+c=0[/tex] to have one distinct solution:
[tex]b^2 - 4ac = 0[/tex]
Here,
a = 2,
b = -k and
c = 18
Putting the values, we get:
[tex](-k)^2 - 4\times 2\times 18 = 0\\\Rightarrow k^2 = 18\times 8\\\Rightarrow k^2 =144\\\Rightarrow k = 12[/tex]
The equation becomes:
[tex]Q(x)=2x^2-12x+18[/tex]
And the one root is:
[tex]2(x^2-6x+9 ) = 0\\\Rightarrow 2(x-3)^2=0\\\Rightarrow x = 3[/tex]
