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Find the zeroes of the quadratic polynomials 2x2 – 8x + 6 and verify the relationship between the zeroes and the coefficients.

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Best answer

Let f(x) = 2x2 – 8x + 6

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

Verification

So, the relationship between the zeroes and the coefficients is verified.

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