Question

Find the zeros of quadratic polynomial √3x^2-5x+√3 and verify the relationship between zeros and the

coefficients.​

Answer 1

Answered

2√3x^2―5x+√3 find the zeros of the quadratic polynomials and verify the relation between zeros and ccoefficient

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

Answer 2

Answer is 5plus/minus 2root3 divided by 2root3