Find K if the difference of roots of the quadratic equation x2 – 5x +(3k-3)=0 is 11.
Answers
Answer:
k is -7
Step-by-step explanation:
given x^2 - 5 x + 3 (k - 1) =0. abare root is given equation
a-b=1. -equation1
using conditions we have a + b =5
ab=3(k-1)
a-b=√a^2+b^2-2ab=√(ab)^2-4ab
(11)^2=(a+b)-4ab
121-25=-12(k-1)=96/12=1-k
k=-7
Answer:
The value of k is -7
Step-by-step explanation:
Given :
The difference of roots of the quadratic equation x² – 5x + (3k - 3) = 0 is 11.
To find :
The value of k
Solution :
The given quadratic equation is x² – 5x + (3k - 3) = 0
- x² coefficient = 1
- x coefficient = -5
- constant term = 3k - 3
Let a and b are the zeroes of the given quadratic equation.
➣ difference of the roots = 11
a - b = 11 ➙ [1]
➣ From the relation between zeroes and coefficients,
- Sum of zeroes = -(x coefficient)/x² coefficient
- Product of zeroes = constant term/x² coefficient
Apply the sum of zeroes relation,
a + b = -(-5)/1
a + b = 5 ➙ [2]
Add both the equations,
a - b + a + b = 11 + 5
2a = 16
a = 16/2
a = 8
Substitute in equation [1],
a - b = 11
8 - b = 11
b = 8 - 11
b = -3
∴ 8 and -3 are the zeroes of the given quadratic equation.
Since they are zeroes of the given quadratic equation, when we substitute the value of zeroes in place of x, the result is zero.
Put x = 8,
x² – 5x + (3k - 3) = 0
8² – 5(8) + (3k - 3) = 0
64 - 40 + 3k - 3 = 0
24 + 3k - 3 = 0
21 + 3k = 0
3k = -21
k = -21/3
k = -7
Therefore, the value of k is -7