(-x2 - 4x - 2) + 2(x2 + x - 4)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) 14(B) 28(C) 36(D) 44
Question
(-x2 - 4x - 2) + 2(x2 + x - 4)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) 14(B) 28(C) 36(D) 44
Solution
First, let's simplify the given expression:
(-x^2 - 4x - 2) + 2(x^2 + x - 4)
= -x^2 - 4x - 2 + 2x^2 + 2x - 8
= x^2 - 2x - 10
So, a = 1, b = -2, and c = -10.
The discriminant of a quadratic equation is given by the formula b^2 - 4ac.
Substituting the values of a, b, and c into the formula, we get:
(-2)^2 - 41(-10)
= 4 + 40
= 44
So, the value of the discriminant is 44 (D).
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