Question

find the zero 9f polynomial p(x)=2x²+7x+6 by splitting the term middle term and verify the relationship between zeros and coefficient​

Answer 1

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By splitting the middle term, we get f(x) = 2 x2 – (2 + 6)x + 6

[∵ – 8 = – (2 + 6) and 2×6 = 12] = 2 x2 – 2x – 6x + 6 = 2x(x – 1) – 6(x – 1) = (2x – 6) (x – 1)

On putting f(x) = 0, we get (2x – 6) (x – 1) = 0 ⇒2x – 6 = 0 or x – 1 = 0 ⇒x = 3 or x = 1

Thus, the zeroes of the given polynomial 2 x2 – 8x + 6 are 1 and 3