Using the discriminant, determine how many real solutions each equation has.No RealSolutions One RealSolution Two RealSolutions0=2x2+x+10=2𝑥2+𝑥+1 −2=−4x2−12x−2=−4𝑥2−12𝑥 12=6x2+x12=6𝑥2+𝑥 0=−34x2−12x−48

The discriminant of a quadratic equation is given by the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0. The discriminant tells us the number of real solutions of the equation: if D > 0, there are two real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Let's calculate the discriminant for each equation:

1. 0 = 2x² + x + 1 Here, a = 2, b = 1, c = 1. D = (1)² - 4*(2)*(1) = 1 - 8 = -7 Since D < 0, there are no real solutions.

2. -2 = -4x² - 12x Here, a = -4, b = -12, c = -2. D = (-12)² - 4*(-4)*(-2) = 144 - 32 = 112 Since D > 0, there are two real solutions.

3. 12 = 6x² + x Here, a = 6, b = 1, c = -12. D = (1)² - 4*(6)*(-12) = 1 + 288 = 289 Since D > 0, there are two real solutions.

4. 0 = -34x² - 12x - 48 Here, a = -34, b = -12, c = -48. D = (-12)² - 4*(-34)*(-48) = 144 - 6528 = -6384 Since D < 0, there are no real solutions.