Question

if the roots of the polynomial
(p)= 3x²-3x+13m-9 are inverse to each other then find tje value of m.​

Answer 1

Given :-

If the roots of the polynomial

(p)= 3x²-3x+13m-9 are inverse to each other

To Find :-

value of m

Solution :-

Let

\mid \pmb{Root \; 1 = \alpha}\mid∣

Root1=α

Root1=α∣

\mid\pmb{Other \; root = inverse }∣

Otherroot=inverse

Otherroot=inverse

Therefore

Root = 1/α

We know that

\bf Product = \alpha \beta = \dfrac{c}{a}Product=αβ=

a

c

\sf \alpha \bigg(\dfrac{1}\alpha\bigg ) = 13m -\dfrac{ 9}3.α(

α

1

)=13m−

3

9

.

Cancelling α

1 = 13m - 9/3

3 = 13m - 9

3 + 9 = `13m

12 = 13m

12/13 = m

Answer 2

Required solution✔

Let one root of the given that other zero is Reciprocal the one zero.

So,

Other zero=1/Alpa.

Given polynomial is 5x2+13x+k=0.

Here,

A=coefficient of x2

B=coefficient of x

And,C=constant term.

Product of zeroes =C/A

Alpha ×1/Alpha =K/5

1=K/5

K=5

Then,

We get k=5.