For the following quadratic equation, find the discriminant.
4, x, squared, minus, 45, x, minus, 269, equals, 7, x, squared, minus, 3, x, plus, 7
4x^2−45x−269 = 7x^2−3x+7
To find the discriminant of a quadratic equation, you first need to rewrite the equation in the standard form: ax^2 + bx + c = 0.
Given equation: 4x^2−45x−269 = 7x^2−3x+7
Step 1: Combine like terms on both sides of the equation.
3x^2 - 42x - 276 = 0
Now we have the equation in the standard form: ax^2 + bx + c = 0, where a = 3, b = -42, and c = -276.
Step 2: Use the formula for the discriminant, which is Δ = b^2 - 4ac.
In this case, b = -42, a = 3, and c = -276.
Δ = (-42)^2 - 4(3)(-276)
= 1764 + 3312
= 5076
Therefore, the discriminant of the given quadratic equation is 5076.