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Question
If (2x – 3) is a factor of 6x2 + x + a, find the value of a. With this value of a, factorise the given expression.
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Solution
Let 2x – 3 = 0
then 2x = 3
⇒ x = `(3)/(2)`
Substituting the value of x in f(x)
f(x) = 6x2 + x + a
`f(3/2) = 6(3/2) + (3)/(2) + a`
= `6 xx (9)/(4) + (3)/(2)`
= `(27)/(2) + (3)/(2) + a`
= `(30)/(2) + a`
= 15 + a
∴ 2x – 3 is the factor
∴ Remainder = 0
∴ 15 + a = 0
⇒ a = –15
Now f(x) will be 6x2 + x – 15
Dividing 6x2 + x – 15 by 2x – 3, we get
`2x - 3")"overline(6x^2 + x - 15)("3x + 5`
6x2 – 9x
– +
10x – 15
10x – 15
– +
x
∴ 6x2 + x – 15 = (2x – 3)(3x + 5).
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