1. **Find the value of the discriminant for the quadratic equation** $2x^2 + 3x - 7 = 0$. The discriminant formula is: $$\Delta = b^2 - 4ac$$ where $a=2$, $b=3$, and $c=-7$. 2. Substitute the values: $$\Delta = 3^2 - 4 \times 2 \times (-7)$$ 3. Calculate step-by-step: $$\Delta = 9 - \cancel{4 \times 2 \times (-7)} + 56$$ 4. Simplify: $$\Delta = 9 + 56 = 65$$ **Answer:** The discriminant is $65$. --- Since the user asked multiple questions, but per instructions, only the first is solved here.