Question

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solve using the quadratic formula.
-t² + 5t = 0
write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
t = or t =

Explanation:

Step1: Identify quadratic coefficients

For $-t^2 + 5t = 0$, we have $a=-1$, $b=5$, $c=0$.

Step2: Recall quadratic formula

The quadratic formula is $t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$.

Step3: Substitute values into formula

$$ t=\frac{-5\pm\sqrt{5^2-4(-1)(0)}}{2(-1)} $$

Step4: Simplify the discriminant

$\sqrt{25 - 0}=\sqrt{25}=5$, so:

$$ t=\frac{-5\pm5}{-2} $$

Step5: Calculate two solutions

First solution (using $+$):

$$ t=\frac{-5+5}{-2}=\frac{0}{-2}=0 $$

Second solution (using $-$):

$$ t=\frac{-5-5}{-2}=\frac{-10}{-2}=5 $$

Answer:

$t = 0$ or $t = 5$