The equation of the smallest degree with real | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Since the coefficients are real,if $1 + i$ is a root,then its conjugate $1 - i$ must also be a root.Let the roots be $\alpha = 1 + i$ and $\beta =

Vedclass · Accepted Answer

$x^2 - 2x + 2 = 0$

Vedclass · Answer

(B) Since the coefficients are real,if $1 + i$ is a root,then its conjugate $1 - i$ must also be a root.Let the roots be $\alpha = 1 + i$ and $\beta = 1 - i$.The sum of the roots is $\alpha + \beta = (1 + i) + (1 - i) = 2$.The product of the roots is $\alpha \beta = (1 + i)(1 - i) = 1^2 - i^2 = 1 - (-1) = 2$.The quadratic equation is given by $x^2 - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Substituting the values,we get $x^2 - 2x + 2 = 0$.

The equation of the smallest degree with real coefficients having $1 + i$ as one of the roots is

Similar Questions

If $x$ is real,the maximum value of $\frac{3x^2 + 9x + 17}{3x^2 + 9x + 7}$ is

When $x+\frac{1}{x}=3$,find $x^{2}+\frac{1}{x^{2}}$.

Let $p, q$ and $r$ be real numbers $(p \ne q, r \ne 0),$ such that the roots of the equation $\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}$ are equal in magnitude but opposite in sign. Then the sum of squares of these roots is equal to:

$A$ two-digit number is four times the sum of its digits and three times the product of its digits. The number is:

If $\log _{10}(x^{2}-6x+45)=2$,then the values of $x$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module