Question

If α+β=5α+β=5
State true or false.

• A. True
• B. False

Answer 1

The correct option is A True

Given
${\alpha }^3+{\beta }^3=35$
Sum of roots, $\alpha +\beta =5$
Cubing both sides,
${\alpha }^3+{\beta }^3+3\alpha \beta (\alpha +\beta )=125$
$35+3\alpha \beta \left(5\right)=125$
$15\alpha \beta =125-35$
$\alpha \beta =\frac{90}{15}$
Product of roots, $\alpha \beta =6$
The equation will be, $x^2-Sx+P=0$ will be
$x^2-5x+6=0$
Answer:1 as the given equation is true.