Question

if sin thita and cis thita are roots of ax^2-bx+c=0 then the relation among a, b, c is​

Answer 1

Answer:

I hope it will be help full for you

Answer 2

Step-by-step explanation:

Given :-

sin thita and cis thita are roots of ax^2-bx+c=0

To find:-

if sin thita and cis thita are roots of ax^2-bx+c=0 then the relation among a, b, c

Solution:-

Given quadratic equation is ax^2-bx+c=0

If Sin Ѳ and Cos Ѳ are the roots then

Sum of the roots = Sin Ѳ +Cos Ѳ

=> -coefficient of x/coefficient of x^2

=>-(-b)/a

Sin Ѳ +Cos Ѳ =b/a ---------(1)

Product of roots =Sin Ѳ Cos Ѳ

=>Constant /coefficient of x^2

Sin Ѳ Cos Ѳ =c/a-----(2)

On squaring equation (1) both sides

(Sin Ѳ +Cos Ѳ )^2 = (b/a)^2

We know that

(a+b)^2 = a^2+2ab+b^2

=>Sin^2 Ѳ +Cos^2 Ѳ +2 Sin Ѳ Cos Ѳ = b^2/a^2

We know that Sin^2 Ѳ +Cos^2 Ѳ = 1

=>1 +2 Sin Ѳ Cos Ѳ = b^2/a^2

=>1+(c/a) = b^2/a^2

=>(a+c)/a = b^2/a^2

=>a^2(a+c )= a×b^2

=>a(a+c)=b^2

=>a^2+ac = b^2

=>a^2-b^2+ac = 0

Answer:-

The relationship among a,b and c is

a^2-b^2+ac = 0

Used formulae:-

• Sum of the roots= -coefficient of x/coefficient of x^2
• Product of roots =Constant /coefficient of x^2
• (a+b)^2 = a^2+2ab+b^2
• Sin^2 Ѳ +Cos^2 Ѳ = 1