Hello, I am really stuck on these 2 questions could someone help please, much appreciated !
1)
2) (I have attemped this one but I do not know if it is right!)
Please help !
Need Help
In your parabola problem, set y = 0 and solve the quadratic equation. These will be the x-intercepts.
$\displaystyle -2x^2+5x+7=0$
$\displaystyle 2x^2-5x-7=0$
Can you finish?
In your second rational equation, you made a mistake at the end of what is shown there. You got a sign wrong.
$\displaystyle x^2-x-2x{\color{red}-2}=x^2-1$
Can you finish from here?
To find the x-coordinates in your first problem, you must solve the quadratic equation for its two values for x. You can do this by factoring, if possible, or by using the quadratic formula:
$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
But $\displaystyle 2x^2-5x-7=0$ factors quite nicely into $\displaystyle (2x-7)(x+1)=0$,
Set each of those factors equal to zero and we have our intercepts.
$\displaystyle 2x-7=0 \ \ or \ \ x+1=0$
$\displaystyle \boxed{x=\frac{7}{2}} \ \ or \ \ \boxed{ x=-1}$
I suggest you check each of these answers by substituting them back into the original quadratic equation.
To finish your second rational equation from where you left it,
$\displaystyle x^2-x-2x-2=x^2-1$
The $\displaystyle x^2$ cancels out and we have
$\displaystyle -3x=1$
$\displaystyle \boxed{x=\frac{1}{3}}$
Check this solution by substituting back into the original rational equation.