in the quadratic equation kx²-6x-1=0 determine the value of k for which the equation has equal roots
Answers
Answer :
The value of k is -9
Step-by-step explanation :
Given,
- the quadratic equation kx²-6x-1=0 has equal roots
To find,
- The value of k
Solution,
we know,
Based on the value of Determinant, we can define the nature of roots.
D > 0 ; real and unequal roots
D = 0 ; real and equal roots
D < 0 ; no real roots i.e., imaginary
The value of Determinant is given by,
D = b² - 4ac
where
b is the coefficient of x
a is the coefficient of x²
c is the constant term
Given quadratic equation,
kx² - 6x - 1 = 0
➙ coefficient of x², a = k
➙ coefficient of x, b = -6
➙ constant term, c = -1
Since it's given - the equation has equal roots.
b² - 4ac = 0
(-6)² - 4(k)(-1) = 0
36 + 4k = 0
4k = -36
k = -36/4
k = -9
∴ The value of k is -9
Answer:
Answer :
The value of k is -9
Step-by-step explanation :
Given,
the quadratic equation kx²-6x-1=0 has equal roots
To find,
The value of k
Solution,
we know,
Based on the value of Determinant, we can define the nature of roots.
D > 0 ; real and unequal roots
D = 0 ; real and equal roots
D < 0 ; no real roots i.e., imaginary
The value of Determinant is given by,
D = b² - 4ac
where
b is the coefficient of x
a is the coefficient of x²
c is the constant term
Given quadratic equation,
kx² - 6x - 1 = 0
➙ coefficient of x², a = k
➙ coefficient of x, b = -6
➙ constant term, c = -1
Since it's given - the equation has equal roots.
b² - 4ac = 0
(-6)² - 4(k)(-1) = 0
36 + 4k = 0
4k = -36
k = -36/4
k = -9
∴ The value of k is -9