Given equation: $$2x^2 - (a+1)x + (a-1)=0$$ I have to find when the difference of two roots is equal to its product, i.e.: $$x_1x_2 = x_1 - x_2.$$ From Vieta's formulas we know that: $$x_1 + x_2 = \frac{a + 1}{2},$$ $$x_1x_2 = \frac{a-1}{2} = x_1 - x_2.$$ Then, solving system of equations: $$x_1 + x_2 = \frac{a + 1}{2}$$ $$x_1 - x_2 = \frac{a-1}{2}$$ we get that $x_1 = \frac{a}{2}$ and $x_2 = \frac{1}{2}$. Then, plugging it into equation $x_1x_2 = x_1 - x_2$ we get: $$\frac{a}{4} = \frac{a - 1}{2}$$ $$4a - 4 = 2a$$ $$2a = 4$$ $$a = 2.$$ Plugging $2$ into previous equation we get that $\frac{1}{2} = \frac{1}{2}$, so solution have to be true. Is my approach correct? If so, are there another ways to solve those kind of problems?
The product of two of of the four roots of the equation <br> is -32, then the value of k is |
If two of the roots of the equation have their product equal to 47 then the value of k is
zusammenhängende Posts
Urheberrechte © © 2024 frojeostern Inc.
