(3x2 - 3x + 3) + (2x2 + 4x - 6)If the expression above is rewritten in the form ax2 + bx + c where a, b, and c are constants, what is the value of the discriminant?(A) 121(B) 61(C) 60(D) 49
Question
(3x2 - 3x + 3) + (2x2 + 4x - 6)If the expression above is rewritten in the form ax2 + bx + c where a, b, and c are constants, what is the value of the discriminant?(A) 121(B) 61(C) 60(D) 49
Solution
First, let's simplify the given expression:
(3x^2 - 3x + 3) + (2x^2 + 4x - 6)
This simplifies to:
5x^2 + x - 3
So, a = 5, b = 1, and c = -3.
The discriminant of a quadratic equation is given by the formula:
D = b^2 - 4ac
Substituting the values of a, b, and c into the formula, we get:
D = (1)^2 - 4*(5)*(-3)
D = 1 + 60
D = 61
So, the value of the discriminant is 61, which corresponds to option (B).
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