Question

If equation of parabola is given by, p(x)=x^2-5x+6, then its factors are
(a) x-3
(b) x-2
(c) Both (a) and (b)
(d) None of these
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Answer 1

Answer:

Given information,

• p(x) = x² - 5x + 6

To Find,

• Factors of the equation (Roots).

Solution,

The roots of the equation of a parabola are points where the parabola touches the x-axis. So when the parabola touches the x-axis, the value of y coordinate will be 0.

Hence, equating y = 0, (p(x) = 0) we get,

⇒ 0 = x² - 5x + 6

⇒ x² - 2x - 3x + 6 = 0

⇒ x ( x - 2 ) - 3 ( x - 2 ) = 0

⇒ ( x - 3 ) ( x - 2 ) = 0

⇒ Roots = +3, +2

Hence the factors of the given parabola are:

• ( x - 3 ) and ( x - 2 )

Hence Option (C) is the correct option.

Answer 2

Given :-

p(x) = x² - 5x + 6

To Find :-

Factors

Solution :-

x² - 5x + 6 = 0

x² - (2x + 3x) + 6 = 0

x² - 2x - 3x + 6 = 0

x(x - 2) - 3(x - 2) = 0

Taking (x - 2) as common

(x - 2)(x - 3) = 0

Hence

(x - 2)(x - 3) are factors of the given equation of the parabola. Option C is correct