Question

solve for h.
2h² - 9h - 11 = 0
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
h =

Explanation:

Step1: Identify coefficients

For the quadratic equation $2h^{2}-9h - 11=0$, where $a = 2$, $b=-9$, $c=-11$.

Step2: Use quadratic formula

The quadratic formula is $h=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 2$, $b=-9$, $c=-11$ into it:
First, calculate the discriminant $\Delta=b^{2}-4ac=(-9)^{2}-4\times2\times(-11)=81 + 88=169$.
Then $h=\frac{-(-9)\pm\sqrt{169}}{2\times2}=\frac{9\pm13}{4}$.

Step3: Find two solutions

For the plus - sign: $h=\frac{9 + 13}{4}=\frac{22}{4}=\frac{11}{2}$.
For the minus - sign: $h=\frac{9-13}{4}=\frac{-4}{4}=-1$.

Answer:

$h=-1,\frac{11}{2}$