JEE Qudratic#10

Algebra Level 3

Let $\alpha$ and $\beta$ be the roots quadratic equation, $0=ax^{2} +bx+c$ If $\Delta= b^{2}-4ac$ and $\alpha +\beta ,\alpha ^{2}+\beta ^{2}, \alpha ^{3}+\beta ^{3}$ are in geometric progression, then which of the following is correct?

c\Delta \neq 0

c\Delta = 0

b\Delta =0

None of these

1 solution

Deepanshu Gupta
Mar 8, 2015

JEE Style :

$Case(a)$ : Let for a time being $\Delta =0$ , then quadratic equation have equal root's , then obviously , required condition is fulfilled, means we get required numbers in GP .

$Case(b)$ :Now again Let for a time being $c=0$ , then this implies given quadratic equation has one root $0$ . So this also fulfilled our required condition , i.e we get required GP .

$Hence$ : $\Delta =0\quad or\quad c=0\\ \Rightarrow \boxed { c\Delta =0 }$

JEE Qudratic#10

1 solution

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