Question

If x =2/3 and x=-3 are the roots of the equation ax^2+7x+b=0, find the values of a and b. ​

Answer 1

Answer:

a=3 and b= -6

Step-by-step explanation:

Now,x=2/3 and -3 are the roots of the equation

ax²+7x+b=0

x=2/3 and x=-3

3x=2 and x+3=0

3x-2=0 and x+3=0

As,they are the roots of the equation ax²+7x+b=0

So, multiple of 3x-2 and x+3 is equal to the given equation

then, (3x-2)(x+3)=3x²+9x-2x-6

=3x²+7x-6

Now, compare the given equation and this equation, we get

a=3 and b= -6

Answer 2

Given:-

• x = 2/3 and x = 3 are the roots of the equation ax² + 7x + b = 0,

To find:-

• Find the values of a and b...?

Solutions:-

• 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.