Algebra Flashcards
In exponent form, what is √x equal to?
x^(1/2)
In exponent form, what is (3√9)^2 equal to?
9^(2/3)
If you were given a^2 + 24a = a^2 +24a + 63, what would you do to prove the two expressions are not the same?
Cancel out the (a^2 + 24a) common factor to get 0=63, which shows that this is impossible.
If the discriminant is 0, what does this mean for the solutions of the equation?
There will only be one solution (0 only has one root)
What does it mean if the discriminant is negative?
The quadratic will have no solutions.
what is log4x = log50t equal to? How would you simplify this?
If logs are on both same and have the same bases and no coefficients, you can remove them. This means the equation simplifies to 4x = 50t.
If the discriminant is negative, what does this mean for the solution?
There will be no solutions (negative numbers have no square roots)
Picture this. You are in a dark alleyway at night, and you hear a noise behind you. You see the equation (f-h)x2 +h - f = 0. It’s brandishing a kitchen knife. Light from a streetlamp hits the knife and bounces off its razor-like blade. What do you do?
Take -1 out as a factor from h - f. Then you can get factorise. ALWAYS LOOK FOR A COMMON FACTOR (even stupid ones like -1. They may come in handy).
Whenever you take the square root of anything…
Remember the root could be negative or positive.
How could you solve the equation 2 to the power of x = 9?
Take the logs of both sides, and because logs are useful, x can be a coefficient of log 2. Divide on your calculator and you have your answer.
How do you add two logs with the same bases?
Multiply the numbers (log3 + log2 = log6)
Is log0 undefined? explain your answer
Yes, as no number raised to anything equals zero.
How do you complete a square
For example, turn x2 + 10x + 22 into a square in the form (x + a) squared + b?
Take the b value (ax2 + bx + c), halve it, and square it to find the c value of the perfect square. (10 divided by 2 squared is 25, so x2 + 10x + 25 -3, so (x + 5) -3)
