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Find the zeroes of the quadratic polynomials x2 + 7x + 10 and verify the relationship between the zeroes and the coefficients.

1 Answer

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Best answer

Let f(x) = x2 + 7x + 10

By splitting the middle term, we get

f(x) = x2 + 5x + 2x + 10 [∵ 7 = 2 + 5 and 2×5 = 10]

= x(x + 5) + 2(x + 5)

= (x + 2) (x + 5)

On putting f(x) = 0 , we get

(x + 2) (x + 5) = 0

⇒ x + 2 = 0 or x + 5 = 0

⇒x = – 2 or x = – 5

Thus, the zeroes of the given polynomial x2 + 7x + 10 are – 2 and – 5

Verification

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

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