Question

Find the zeroes of the following quantity polynomials and verify the relationship between the zeroes and the coefficients (2)2√2x^2-9x+5√2

Answer 1

Given a quadratic equation,

⇒ 2√2x² - 9x + 5√2 = 0

First, we have to find the zeroes of the given qudratic equation and would have to verify the relationship between the zeroes and the coefficients.

Solving the given quadratic equation by splitting the middle term,

⇒ 2√2x² - 9x + 5√2 = 0

⇒ 2√2x² - 4x - 5x + 5√2 = 0

⇒ 2√2x (x - √2) - 5( x - √2 ) = 0

⇒ (x - √2)(2√2x - 5) = 0

Here, x = √2 & 5/2√2

Now, We need to verify the relationship between the zeroes and the coefficients,

Comparing the given quadratic equation with the standard form of quadratic equation i.e., ax² + bx + c = 0 , we get

• a = 2√2
• b = -9
• c = 5√2

Verification :-

We know,

⇒ Sum of zeroes = - b / a

⇒ √2 + 5/2√2 = - (-9) / 2√2

⇒ ( 2√2 × √2 + 5 ) / 2√2 = 9/2√2

⇒ 9 / 2√2 = 9 / 2√2

Also,

⇒ Product of zeroes = c / a

⇒ √2 × 5/2√2 = 5√2 / 2√2

⇒ 5 / 2 = 5 / 2

Hence, Verified.