From x2− 5x + 6 = 0, find the roots using… | Answer

Subject

গণিত

Topic

Algebra

ক)

2 and 3

খ)

−2 and −3

গ)

1 and 6

ঘ)

3 and 5

Correct answer: Option 1 (2 and 3). Explanation (textbook style, using Vieta and factoring): For the quadratic

x^{2}-5x+6=0

(here

a=1,\;b=-5,\;c=6

), Vieta's formulas state that if the roots are

r_1,r_2

then

\;r_1+r_2=-\dfrac{b}{a}

and

\;r_1r_2=\dfrac{c}{a}

. Thus

r_1+r_2=-\dfrac{-5}{1}=5

and

r_1r_2=\dfrac{6}{1}=6

. We need two numbers whose sum is

5

and product is

6

; these numbers are

2

and

3

. Therefore the roots are

2

and

3

. Equivalently, factor the quadratic:

x^{2}-5x+6=(x-2)(x-3)

. Setting this to zero gives

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

, so

x=2

x=3

From x2− 5x + 6 = 0, find the roots using Vieta.