If x=2/3 and x= -3 are the roots of the equation ax^2+7x+b=0. find the value of a and b.
Answers
Given:
x = 2/3 and x = -3 are the roots of the equation ax² + 7x + b = 0,
Find:
Values of a and b
Solution:
ax² + 7x + b = 0
x = 2/3 or x = -3
We have to fine a and b.
Now,
If x = 2/3 is a root of the equation.
=> ax² + 7x + b = 0
=> a(2/3)² + 7(2/3) + b = 0
=> 4a/9 + 14/3 + b = 0
=> (4a + 42 + 9b)/9 = 0
=> a = (-9b - 42)/4 ..........(i).
Also,
if x = -3 is a root of the equation.
=> ax² + 7x + b = 0
=> a(-3)² + 7(-3) + b = 0
=> 9a - 21 + b = 0 .............(ii).
Now,
The multiple equation (ii). by 9 and then Subtract equation (i). we get.
=> 81a + 9b - 189 - 4a - 9b - 42 = 0
=> 77a - 231 = 0
=> a = 231/77
=> a = 3
Now, putting the value of a in Eq. (ii).
=> 9a + b - 21 = 0
=> 9(3) + b - 21 = 0
=> 27 + b - 21 = 0
=> 6 + b = 0
=> b = - 6
Hence, the value of a is 3 and b is -6.
I hope it will help you.
Regards.
Answer:
Let the present age of Aaron be 'x' years.
Let the present age of Ron be 'y' years
Aaron is 5 years younger than Ron
=> x = y + 5 .......(i).
4 years later Aaron will be twice as old as Ron
Aaron's age = (x+ 4) years
Ron's age = (y+4) years
=> (x + 4) = 2(y + 4
Step-by-step explanation: