Question

Find zeroes of polynomial x² + 7x + 10.

Answer 1

Answer: -2 and -5

Step-by-step explanation:

Let p(x) be x² + 7x + 10

Let's find the roots using splitting the middle term method.

x² + 7x + 10 = 0

x² + 2x + 5x + 10 = 0

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

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

So, x = -2 or -5

Therefore, α = -2 and β = -5 are the zeroes of given polynomial.

Answer 2

$\qquad \bf{ {x}^{2} + 7x + 10 = 0 } \\ \\ \sf{by \: middle \: term \:splitting \: method } \\ \\ \longrightarrow \: \sf{ {x}^{2} + (5 + 2)x + 10 = 0} \\ \\ \longrightarrow \: \sf{ {x}^{2} + 5x + 2x + 10 = 0} \\ \\ \longrightarrow \: \sf{x(x + 5) + 2(x + 5) = 0 } \\ \\ \longrightarrow \: \sf{(x + 5)(x + 2) = 0}$

x + 5 = 0

→ x = –5

x + 2 = 0

→ x = –2

So, –5 and –2 are the zeroes of the given polynomial .