## Filters

Q&A - Ask Doubts and Get Answers
Q

# Solve! - Complex numbers and quadratic equations - BITSAT

Let and be the roots of equation are in A.P. and   then the value of is ?

• Option 1)

• Option 2)

• Option 3)

• Option 4)

124 Views
N

As we have learned

Sum of Roots in Quadratic Equation -

$\alpha +\beta = \frac{-b}{a}$

- wherein

$\alpha \: and\beta$ are root of quadratic equation

$ax^{2}+bx+c=0$

$a,b,c\in C$

Product of Roots in Quadratic Equation -

$\alpha \beta = \frac{c}{a}$

- wherein

$\alpha \: and\ \beta$ are roots of quadratic equation:

$ax^{2}+bx+c=0$

$a,b,c\in C$

@1449

$|\alpha -\beta | = \left | \frac{\sqrt{q^2}-4pr}{p} \right |$

$\left ( \because \left | \frac{\sqrt{D}}a{} \right | \right )$

Also $\frac{\alpha +\beta }{\alpha \beta }= 4$

$\Rightarrow \frac{-q}{r}= 4$

$\Rightarrow q = -4r ....(1)$

$= \sqrt{16(\frac{r}{p})^2-(4\frac{r}{p})}$

Also p+r =2q

$\Rightarrow p+r = -8r \Rightarrow r/p = -1/9$

$\therefore \frac{\left | \alpha -\beta \right |}{16\times 1/81+4/9}= \sqrt{\frac{52}{81}}=\frac{2\sqrt{13}}{9}$

Option 1)

Option 2)

Option 3)

Option 4)

Exams
Articles
Questions