How do you evaluate ∫∞0xx−−√e−xdx please answer please mathematics
Answers
Answer:
Answer:
The relationship between zeros and coefficients of given polynomial is verified.
Step-by-step explanation:
Polynomial = 5x² – 6√2x + 2
Find zeros of the given polynomial by factorizing the polynomial.
\longrightarrow⟶ 5x² – 6√2x + 2
\longrightarrow⟶ 5x² – 5√2x – √2x + 2
\longrightarrow⟶ 5x(x – √2) – √2(x – √2)
\longrightarrow⟶ (5x – √2)(x – √2)
Zeros will be =
\longrightarrow⟶ 5x – √2 = 0
\longrightarrow⟶ 5x = √2
\longrightarrow⟶ x = √2/5
\longrightarrow⟶ x – √2 = 0
\longrightarrow⟶ x = √2
The zeros are √2/5 and √2.
______________________
Verifying the relationship of zeros and coefficients :
Let the α and β be zeros.
In the polynomial,
a = 5
b = -6√2
c = 2
Sum of zeros :
\longrightarrow⟶ √2/5 + √2
\longrightarrow⟶ √2/5 + 5√2/5
\longrightarrow⟶ 6√2/5 ---- (I)
\longrightarrow⟶ α + β = -b/a
\longrightarrow⟶ α + β = -(-6√2)/5
\longrightarrow⟶ α + β = 6√2/5 ---- (II)
Product of zeros :
\longrightarrow⟶ √2/5 × √2
\longrightarrow⟶ 2/5 ---- (III)
\longrightarrow⟶ α β = c/a
\longrightarrow⟶ α β = 2/5 ---- (IV)
I and II are equal
III and IV are equal
Hence, the relationship between zeros and coefficients of given polynomial is verified.