Question

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

Answer 1

Answer:

if x =2/3 and x = -3 are roots of the quadratic equation ax^2 + 7x + b = 0, find the values of a =3 &b=-6

Answer 2

Answer:

a = 3 & b = (-6)

Step-by-step explanation:

Substituting x=(-3) in the quadratic equation:

✓ 9a+7*(-3)+b=0

✓ 9a+b-21=0 -------------- Equation (1)

Substituting x=(2/3) in the quadratic equation:

✓ a*(4/9)+b+(14/3)=0

Taking LCM

✓ 4a+9b+(14*3)=0

✓ 4a+9b+42=0 -------------- Equation (2)

Multiplying equation (1) by 9 and subtracting it from equation (2), we get

✓ 4a-81a+9b-9b+42-(-189)=0

✓ -77a+231=0

✓ a=231/77

✓ a=3

Now substituting a in equation (1) we get,

✓ 9*(3)+b-21=0

✓ 27+b-21=0

✓ b=(-6)

Hence, a = 3 & b = (-6)

Hope this helps!

Feel free to ask me if you still have any doubts.