solve the equation. y^2 - 9y + 14 = 0?

Some expressions can be factored to find the answers. In this case, the constant 14 has a positive sign and the y coefficient is negative.

This tells you two things: 1) the signs in the two factors are the same and 2) they are negative.

So far, we know:

(y - ??)(y - ??) = y^2 -9y + 14 = 0

Now all you need is two factors of 14 which total up to 9 (to make the y coefficient work out to be -9). The values 2 and 7 will do nicely:

(y - 2)(y - 7) = y^2 -9y + 14 = 0

From that factoring, the value of the expression will be zero when either of these two factors is zero.

This occurs at the roots of the equation, 2 and 7.

(y - 7)(y - 2) = 0
y = 7 , y = 2

y^2-9y+14=0

(y-2)(y-7)=0

y=2 or 7

(y - 7)(y - 2)=0

either y=7 or y=2

y^2 - 9y + 14 = 0

y^2 - 7y -2y +(-7)(-2) = 0

y(y -7) -2(y -7) = 0

(y -7)(y -2) = 0

y - 7 = 0 , y = 7

y -2 = 0 , y = 2

Actually we have to factorise it!

so
(y)^2 -7y -2y +(-7)(-2)

by identity
(x+a)(x+b)=x^2+ax+bx+ab

so this implies
(y-7)(y-2)

Hope it Helps!!!
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y^2 - 9y + 14 = 0
y^2 - 2y - 7y + 14 = 0
(y^2 - 2y) - (7y - 14) = 0
y(y - 2) - 7(y - 2) = 0
(y - 2)(y - 7) = 0

y - 2 = 0
y = 2

y - 7 = 0
y = 7

∴ y = 2 , 7