Search any question & find its solution
Question:
Answered & Verified by Expert
If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-2 x+4=0$, then what is the value of $\alpha^{3}+\beta^{3} ?$
Options:
Solution:
1436 Upvotes
Verified Answer
The correct answer is:
$-16$
Let $\alpha$ and $\beta$ are the roots of $x^{2}-2 x+4=0$ sum of roots $=\alpha+\beta=2$, product $=\alpha \beta=4$
Now, $\alpha^{3}+\beta^{3}=(\alpha+\beta)^{3}-3 \alpha \beta(\alpha+\beta)=2^{3}-3 \times 4 \times 2$
$=8-24=-16$
Now, $\alpha^{3}+\beta^{3}=(\alpha+\beta)^{3}-3 \alpha \beta(\alpha+\beta)=2^{3}-3 \times 4 \times 2$
$=8-24=-16$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.