if a,b are the zeros of x^-6x+k=0 what is the value of k if 3a + 2b =20
Answers
Appropriate Question :
If a, b are the zeroes of x²-6x+k=0, then what is the value of k if 3a + 2b =20
Answer :
The required value of k is -16
Step-by-step explanation :
Given :
- a, b are the zeroes of x² - 6k + k = 0
- 3a + 2b = 20
To find :
the value of k
Solution :
To solve this question, we must know the relation between sum of zeroes and coefficients of quadratic equation.
Sum of zeroes = -(x coefficient)/x² coefficient
For the given quadratic equation, x² - 6x + k = 0
x² coefficient = 1
x coefficient = -6
constant term = k
Sum of zeroes = -(-6)/1
a + b = 6 ➙ [1]
3a + 2b = 20 ➙ [2]
Multiplying the equation [1] by 3, we get
3(a + b) = 3(6)
3a + 3b = 18 ➙ [3]
Now, subtract equation [2] from equation [3],
3a + 3b - (3a + 2b) = 18 - 20
3a + 3b - 3a - 2b = -2
b = -2
So, one of the zeroes = -2
Since it's a zero, when we substitute x = -2, the result is zero.
x² - 6x + k = 0
(-2)² - 6(-2) + k = 0
4 + 12 + k = 0
16 + k = 0
k = -16
∴ The value of k is -16