For ax2+ bx + c = 0 with roots r1, r2, st… | Answer

Subject

গণিত

Topic

Algebra

ক)

r1 + r2 = b/a, r1 r2 = −c/a

খ)

r1 + r2 = −b/a, r1 r2 = c/a

গ)

r1 + r2 = −c/a, r1 r2 = b/a

ঘ)

r1 + r2 = c/a, r1 r2 = −b/a

For the quadratic equation

ax^2+bx+c=0

(with

a\neq0

) let the roots be

r_1

and

r_2

. Then the polynomial can be written in factored form

a(x-r_1)(x-r_2)=ax^2-a(r_1+r_2)x+a\,r_1r_2.

Comparing coefficients with

ax^2+bx+c

gives

-a(r_1+r_2)=b\quad\Rightarrow\quad r_1+r_2=-\frac{b}{a},

a\,r_1r_2=c\quad\Rightarrow\quad r_1r_2=\frac{c}{a}.

Thus Vieta’s relations are

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

and

r_1r_2=\dfrac{c}{a}

. (If

a=1

these reduce to

r_1+r_2=-b

and

r_1r_2=c

For ax2+ bx + c = 0 with roots r1, r2, state Vieta’s relations.