Question

If the root of the equation ax²+bx +c=0 are in the ratio m:n then​

Answer 1

Step-by-step explanation:

The given equation is

ax^2+bx+c=0ax

2

+bx+c=0

It is given that the roots of the equation ax²+bx+c=0 are in the ratio m:n.

Let the roots of given equation are mx and nx.

We know that the sum of roots is equal to -b/a and the product of roots is c/a.

mx+nx=b\Rightarrow x(m+n)=-\frac{b}{a}\Rightarrow x=-\frac{b}{a(m+n)}mx+nx=b⇒x(m+n)=−

a

b

⇒x=−

a(m+n)

b

....(1)

mx\times nx=\frac{c}{a}\Rightarrow mnx^2=\frac{c}{a}mx×nx=

a

c

⇒mnx

2

=

a

c

.....(2)

Substitute the value of x from equation (1) in equation (2).

mn(-\frac{b}{a(m+n)})^2=\frac{c}{a}mn(−

a(m+n)

b

)

2

=

a

c

mnb^2=\frac{a^2c(m+n)^2}{a}mnb

2

=

a

a

2

c(m+n)

2

mnb^2=ac(m+n)^2mnb

2

=ac(m+n)

2

Answer 2

Answer:

refer to the attachment...

Step-by-step explanation:

hope it helps...