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In the product of (2x^2 + 4x + 7)(ax^2 -...

In the product of `(2x^2 + 4x + 7)(ax^2 - 4x - b)`, the coeffiecient of` x^4` is `6` and that of `x` is `4`. Find a and b.

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`(2x^2+4x+7)(ax^2-4x-b)`
In this product, term involving `x^4` will be,
`(2x^2)(ax^2) = 2ax^4`
`:. 2a = 6`
`=> a= 3`
In this product, term involving `x` will be,
`4x(-b)+(-4x)*7 = -4bx-28x = (-4b-28)x`
`:. -4b-28 = 4`
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