What polynomial function must be added to the product of f(x)=2-x and g(x)=x-3 to obtain the function h(x)=x²-3x+4?
Answers
Answer:
Quadratic Equation
A quadratic equation in a variable xx is an equation which is of the form ax^2 + bx + c = 0ax
2
+bx+c=0 where constants a, b and c are all real numbers and a \neq 0.a
=0.
In case of a quadratic equation ax^2 + bx + c = 0ax
2
+bx+c=0 the expression b^2 + 4acb
2
+4ac is called the discriminant.
Let's first solve the given equation!
\begin{gathered}\implies 10x^2 + x = 1 \\ \\ \implies 10x^2 + x - 1 = 0\end{gathered}
⟹10x
2
+x=1
⟹10x
2
+x−1=0
Now, comparing the given equation with the standard form of quadratic equation, we get:
\qquad a = 10, \: b = 1, \: c = 1a=10,b=1,c=1
Now using the discriminant formula and solving the equation, we get:
\begin{gathered} \implies {1}^{2} + 4 \times 10 \times 1 \\ \\ \implies 1 + 4 \times 10 \times 1 \\ \\ \implies 1 + 40 \\ \\ \implies \boxed{41}\end{gathered}
⟹1
2
+4×10×1
⟹1+4×10×1
⟹1+40
⟹
41
Hence, the required answer is 41
Answer:
f(x)=2-x
2-x=0
x=-2
g(x)=x-3
x-3=0
x=3
h(x)=x²-3x+4
=(-2)²-3(3)+4
=(4)-9+4
= 4-5
=-1