Question

If x= 2/3,
-3
-
are the roots
of equation
ax² + 7x+ b =0, find
the value of a and b​

Answer 1

Answer:

when x=2/3

ax^2+7x+b=0

a (2/3)^2+7 (2/3)+b=0

a (4/9)+14/3+b=0

(4a/9)+(14/3)+b=0

taking LCM

(4a+42+9b)/9=0

4a+42+9b=0

4a+9b= -42 -------------------(i)

when x = -3

ax^2 + 7x + b =0

a (-3)^2 + 7 (-3)+b=0

a (9)-21+b=0

9a-21+b=0

9a+b=21 -----------------(ii)

now,from (i) and (ii)

4a+9b= -42

9a+b = 21

in equation (ii)×9 and subtract euation (i)

81a + 9b = 189

4a + 9b = -42

- - +

-------------------------

77a =231

a=3

now put the value of a =3 in equation (ii)

9a + b =21

9 (3) + b = 21

27 + b =21

b = 21-27

b = -6

so, a = 3 and b = -6

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