Question

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

Answer 1

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

Answer 2

Step-by-step explanation:

Given:

• 2√3x² – 5x + √3

To Find:

• Zeros of the polynomials and to verify the relation between zeros and coefficient.

Solution: Let the given polynomial be denoted by f(x). Then,

→ f(x) = 2√3x² – 5x + √3

→ 2√3x² – 3x – 2x + √3 [ By middle term splitting ]

→ √3x (2x – √3) – 1 (2x – √3)

→ (√3x – 1) (2x – √3)

∴ f(x) = 0 => (√3x – 1) (2x – √3) = 0

=> √3x – 1 = 0 or 2x – √3 = 0

=> x = 1/√3 or x = √3/2

So, The zeros of f(x) are 1/√3 and √3/2

★ Sum of zeros = {1/√3 + √3/2}

→ 2+3/2√3

→ 5/2√3 = –( coefficient of x)/(coefficient of x²)

★ Product of zeros = 1/√3 x √3/2

→ √3/2√3 = Constant term / Coefficient of x²