Question

sa se determine a apartine lui R, stiind ca 2x1+5x1x2=0, unde x1,x2 sunt solutiile ecuatiei x^2-3x+a=0

Answer 1

$x^2-3x+a = 0\\ \\ 2x_1 + 5x_1x_2 = 0 \Rightarrow 2x_1 + 5\cdot \dfrac{a}{1} = 0 \Rightarrow 2x_1 = -5a \Rightarrow \\ \\ \Rightarrow x_1 = -\dfrac{5a}{2} \\ \\ x_1^2-3x_1+a = 0 \Rightarrow \Big(-\dfrac{5a}{2}\Big)^2 -3\cdot \Big(-\dfrac{5a}{2}\Big) + a = 0 \Rightarrow \\ \\ \Rightarrow \dfrac{25a}{4} + \dfrac{15a}{2} + a = 0 \Rightarrow 25a+30a+4a = 0 \Rightarrow 59a = 0 \Rightarrow \\ \\ \Rightarrow \boxed{a = 0}$