Q. For the following quadratic equation, find the discriminant.−9x2−70x−245=−4x2Answer:
Simplify Quadratic Equation: First, we need to simplify the quadratic equation by moving all terms to one side to get it into standard form ax2+bx+c=0. −9x2−70x−245=−4x2 Add 4x2 to both sides to combine like terms. (−9x2+4x2)−70x−245=0 −5x2−70x−245=0
Find Discriminant: Now that we have the quadratic equation in standard form, we can find the discriminant. The discriminant of a quadratic equation ax2+bx+c is given by b2−4ac. For our equation, a=−5, b=−70, and c=−245.
Calculate Discriminant: Calculate the discriminant using the values of a, b, and c. Discriminant = b2−4ac Discriminant = (−70)2−4(−5)(−245)
Perform Calculations: Perform the calculations.Discriminant = 4900−4(−5)(−245)Discriminant = 4900−4900
Final Result: After calculating, we find that the discriminant is 0. Discriminant = 0