If 4x^2+9=kx, what value of k will produce equal roots?
the answer is 12 but i don't understand how you get it, please help!
4 x ^ 2 + 9 = kx
4 x ^ 2 - k x + 9 = 0
Quadratic equation has two real roots, if Discrininant Ä = 0
Ä = b ^ 2 - 4 * a * c
In this case :
a = 4
b = - k
c = 9
Ä = b ^ 2 - 4 * a * c
Ä = ( - k ) ^ 2 - 4 * ( 4 ) * 9
Ä = k ^ 2 - 144 = 0
k ^ 2 - 144 = 0
k ^ 2 = 144
k = sqrt ( 144 )
k = ± 12
For k = - 12
4 x ^ 2 + 9 = k x
not equal becouse left side of equation are positive ( 4 x ^ 2 + 9 ) are allways great of 0 ) ,and right side of equation are negative.
So solution are k = 12
Quadratic equation has two real equals roots, if Discrininant Ä = 0
Ä = greek letter Delta
To find the value of k that will produce equal roots in the equation 4x^2 + 9 = kx, we can use the discriminant of the quadratic equation. The discriminant is the expression inside the square root sign (√) in the quadratic formula.
The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the given equation, a = 4, b = -k, and c = 9.
For equal roots, the discriminant (b^2 - 4ac) should be equal to zero.
Substituting the values into the discriminant:
0 = (-k)^2 - 4 * 4 * 9
Simplifying the expression:
0 = k^2 - 144
Rearranging the equation, we get:
k^2 = 144
Taking the square root on both sides:
√(k^2) = √(144)
Since we are looking for the value of k, we take the positive square root:
k = √(144)
Simplifying:
k = 12
Therefore, the value of k that will produce equal roots is 12.