Final answer:
The discriminant of the polynomial 2x²+3x−7 is 65, which is found using the discriminant formula b² - 4ac and plugging in the values a=2, b=3, and c=-7.
Step-by-step explanation:
To find the discriminant of the polynomial 2x²+3x−7, we use the standard formula for the discriminant of a quadratic equation ax²+bx+c, which is b² - 4ac.
For our specific polynomial, a=2, b=3, and c=-7. Plugging these values into the formula, we get:
−(3² - 4×2×(-7)) = 9 + 56 = 65.
The discriminant of a quadratic polynomial in the form ax²+bx+c is given by the formula Δ=b²-4ac.
In this case, the polynomial is 2x²+3x-7, so a=2, b=3, and c=-7.
Substituting these values into the formula, we have Δ=3²-4(2)(-7)=9+56=65.
Therefore, the discriminant of the polynomial 2x²+3x-7 is 65.
Thus, the discriminant of the polynomial is 65, which corresponds to option (c).