awalters2023
Answered

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(3 x + a )(2 x – 3) = 6 x ^2+bx+6

find the values of a and b

Sagot :

Eduard22sly

Answer:

a = –2

b = –13

Explanation:

(3x + a )(2x – 3) = 6x² + bx + 6

The value of a and b can be obtained as follow:

(3x + a )(2x – 3)

Expand

3x(2x – 3) + a(2x – 3)

6x² – 9x + 2ax – 3a

6x² – (9 – 2a)x – 3a

But:

(3x + a )(2x – 3) = 6x² + bx + 6

Therefore,

6x² – (9 – 2a)x – 3a = 6x² + bx + 6

From the above,

–3a = 6

Divide both side by –3

a = 6/–3

a = –2

b = –(9 – 2a)

But

a = –2

b = –(9 – 2×–2)

b = –(9 + 4)

b = –(13)

b = –13

SUMMARY:

a = –2

b = –13

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