The general form of a polynomial is: x² + bx + c = 0. Substituting the roots,
3² + b(3) + c = 0
3b + c = -9 --> eqn 1
(5 + √5)² + (5 +√5)(b) + c = 0
(5+√5)b + c = -30-10√5 --> eqn 2
Solving both equations simultaneously by subtracting eqn 2 from eqn 1,
(-2 - √5)b = 21 + 10√5
b = -8 - √5
Using eqn 1,
3(-8 - √5) + c = -9
-24 - 3√5 + c = -9
c = -9 + 24 + 3√5
c = 15 + 3√5
Hence, the polynomial is: <em>f(x) = x² + (-8 - √5)x + (15 + 3√5)</em>.
Answer:
coefficient of the term of degree 4 in this polynomial is 3
Step-by-step explanation:
Answer:
x= -1 or x = -2
Step-by-step explanation:
Your equation:
(x−3)^3−(x−1)^3+7x^2=7(3x−4)
Step 1: Simplify both sides of the equation.
x^2+24x−26=21x−28
Step 2: Subtract 21x-28 from both sides.
x^2+24x−26−(21x−28)=21x−28−(21x−28)
x^2+3x+2=0
Step 3: Factor left side of equation.
(x+1)(x+2)=0
Step 4: Set factors equal to zero.
x+1=0 or x+2=0
which equals to x=−1 or x=−2
