find the zeros of the polynomial and verify the relationship between the zeros and coefficients 3 x square - 5 Pls Answer:(
Answers
Step-by-step explanation:
Answer
The zeroes of the polynomial are
√3/2 and 1/√3
Step by step explanation
Given , the quadratic polynomial
2√3x² - 5x +√3
By factorization we have
2√3x² -5x + √3
=2√3x² - 2x - 3x +√3
= 2x(√3x - 1) -√3(√3x - 1)
=(2x - √3)(√3x- 1)
Thus the zeroes of the quadratic polynomial are
⇒2x - √3=0
⇒2x =√3
⇒x = √3/2
and
⇒√3x -1=0
⇒x = 1/√3
Verification of the zeroes of the polynomial
Sum of the roots = -coefficient of x/coefficient of x²
⇒√3/2 + 1/√3= -(-5)/2√3
⇒(√3×√3+2)/2√3= 5/2√3
⇒(3+2/2)√3= 5/2√3
⇒5/2√3= 5/2√3
And again
Product of the roots = costant term/coefficient of x²
⇒(√3/2)×(1/√3)= √3/2√3
⇒1/2 = 1/2
Thus verified
The zeroes of the polynomial are
√3/2 and 1/√3
Step by step explanation
Given , the quadratic polynomial
2√3x² - 5x +√3
By factorization we have
2√3x² -5x + √3
=2√3x² - 2x - 3x +√3
= 2x(√3x - 1) -√3(√3x - 1)
=(2x - √3)(√3x- 1)
Thus the zeroes of the quadratic polynomial are
⇒2x - √3=0
⇒2x =√3
⇒x = √3/2
and
⇒√3x -1=0
⇒x = 1/√3
Verification of the zeroes of the polynomial
Sum of the roots = -coefficient of x/coefficient of x²
⇒√3/2 + 1/√3= -(-5)/2√3
⇒(√3×√3+2)/2√3= 5/2√3
⇒(3+2/2)√3= 5/2√3
⇒5/2√3= 5/2√3
And again
Product of the roots = costant term/coefficient of x²
⇒(√3/2)×(1/√3)= √3/2√3
⇒1/2 = 1/2
Thus verified