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प्रश्न
By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x2 + 5x – 3.
उत्तर
Let x + 3 = 0 then x = – 3
Substituting the value of x in f(x)
f(x) = 2x2 + 5x – 3
= 2(–3)2 + 5(–3) –3
f(–3) = 18 – 15 – 3 = 0
∵ Remainder = 0,
then x + 3 is a factor
Again let 2x - 1 = 0,
then x = `(1)/(2)`
Substituting the value of x in f(x),
f(x) = 2x2 + 5x – 3
`f(1/2) = 2(1/2)^2 + 5(1/2) -3`
= `2 xx (1)/(4) + (5)/(2) - 3`
= `(1)/(2) + (5)/(2) - 3` = 0
∵ Remainder = 0,
∴ 2x – 1 is also a factor
Hence, proved.
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