
If one root of the is 3 – i; where , then the other root is
( a ) 3 + i
( b ) 3 + 2i
( c ) -1 + i
( d ) -1 - i
Answer
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Hint: We will use the results based on of relationship between roots of quadratic equation to evaluate the values of , which is given by the relation of coefficients of quadratic equation such as for quadratic equation where
Complete step-by-step answer:
Now, firstly we will find the coefficients of , and constant c from the given polynomial by comparing it with the general form of quadratic polynomial which is expressed as .
On comparing given polynomial with general form of quadratic polynomial, we get coefficients of quadratic polynomial equals to,
a = i, b = -2( i + 1 ), c = 2 - i
let, be two roots of quadratic polynomials.
Now,
Here, we know that ……( i ),
So, we can obtain the value of which represents the another root of quadratic equation, easily by substituting the values of b and a in an equation ( i )
Substituting values of a = i and b = -2( i + 1 ) in , we get
On simplifying signs, we get
We know, as it is one of the root of quadratic equation, then substituting value of in , we get
Multiplying numerator and denominator on right hand side by i, we get
On solving, we get
As , so
On simplifying, we get
So, the correct answer is “Option D”.
Note: Remember these formulae as they are very helpful in solving questions. While calculating the coefficients of a quadratic equation, try to avoid signs of error as this makes the answer incorrect. Simplification of signs should be done carefully. We can also use the product of the root formula and simplify to get the answer.
Complete step-by-step answer:
Now, firstly we will find the coefficients of
On comparing given polynomial with general form of quadratic polynomial, we get coefficients of quadratic polynomial
a = i, b = -2( i + 1 ), c = 2 - i
let,
Now,
Here, we know that
So, we can obtain the value of
Substituting values of a = i and b = -2( i + 1 ) in
On simplifying signs, we get
We know,
Multiplying numerator and denominator on right hand side by i, we get
On solving, we get
As
On simplifying, we get
So, the correct answer is “Option D”.
Note: Remember these formulae as they are very helpful in solving questions. While calculating the coefficients of a quadratic equation, try to avoid signs of error as this makes the answer incorrect. Simplification of signs should be done carefully. We can also use the product of the root formula and simplify to get the answer.
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