Question

Find the zeroes of the quadratic polynomial 5x^2

-6√2x+2 and verify the

relation between zeroes and coefficients of quadratic polynomial.​

Answer 1

Given :

• Quadratic polynomial 5x² - 6√2x + 2

To Find :

• The zeros of quadratic polynomial & verify the relation between zeroes and coefficients of quadratic polynomial.

According to the question,

⇒ 5x² - 6√2x + 2

⇒ 5x² - 5√2x - √2x + 2

⇒ 5x( x - √2) - √2(x - √2)

⇒ (5x - √2) (x - √2)

So,

• x = √2/5
• x = √2

We know that,

• Sum of zeros = α + β

⇒ α + β

⇒ √2/ 5 + √2

⇒ √2 + 5√2/ 5

⇒ 6√2/5

• Product of zeros = αβ

⇒ αβ

⇒ √2/ 5 × √2

⇒ 2/5

Now,

• α + β = -b/a

⇒ -(-6√2 /5)

⇒ 6√2/ 5

• αβ = c/a

⇒ 2/5

Hence,verified!