The solutions are - 0.8 and 1
Step-by-step explanation:
In the quadratic equation ax² + bx + c = 0
Assume that the solutions of the equations are m and n
∵ 5x² - x - k = 0
- By comparing it by the form above
∴ a = 5, b = -1 , c = -k
- Use the rule of the sum of the two solutions above
∵ The sum of the two solutions = [tex]\frac{-b}{a}[/tex]
∴ The sum of the two solutions = [tex]\frac{-(-1)}{5}=0.2[/tex]
∵ The two solutions are m and n
∴ m + n = 0.2 ⇒ (1)
∵ The difference of the two solutions is 1.8
∴ m - n = 1.8 ⇒ (2)
Now we have a system of equations to solve
Add Equations (1) and (2) to eliminate n
∴ 2m = 2
- Divide both sides by 2
∴ m = 1
- Substitute the value of m in equation (1) to find n
∴ 1 + n = 0.2
- Subtract 1 from both sides
∴ n = -0.8
The solutions are - 0.8 and 1
If you want to find the value of k
∵ The product of the solutions is [tex]\frac{c}{a}[/tex]
∴ The product of the solutions = [tex]\frac{-k}{5}[/tex]
∵ m × n = 1 × (-0.8) = - 0.8
- Equate [tex]\frac{-k}{5}[/tex] by - 0.8
∴ [tex]\frac{-k}{5}=-0.8[/tex]
- Multiply both sides by -5
∴ k = 4
∴ The equation is 5x² - x - 4 = 0
Learn more:
You can learn more about the quadratic equation in brainly.com/question/2364381
#LearnwithBrainly
Answer:
x = 1; x = -0.8
Step-by-step explanation:
Here is a simpler approach if needed for future students:
5x^2-x-k = 0,
System of Equations: x1 - x2 = 1.8 & x1 + x2 = 1/5 = 0.2 (if x1 and x2 are roots)
Now let's add the two:
x1 - x2 = 1.8
+ x1 + x2 = 0.2
----------------------
2x1 = 2,
x1 = 2/2 = 1
- x2 = 1.8 - 1 = 0.8 => x2 = -0.8
