Question

αβ are zeros of x²-7x+9 then α-β is​

Answer 1

$\sf\underline{here \: is \: your \: answer}$

GIVEN,

$\sf\pink{ \alpha \beta \: are \: zeros}$

THESE ARE ZEROES OF ²–7+9

Answer 2

Given:

α and β are the zeroes of the polynomial x²-7x+9.

To Find:

The value of α-β is?

Solution:

The given problem can be solved using the concepts of quadratic equations.

1. Consider a quadratic equation ax² + b x + c = 0, let the roots of the quadratic equation be p and q. Then,

• Sum of the roots = p + q = (-b/a)
• Product of the roots = p x q = (c/a)

2. Using the above formulae the value of α-β can be calculated.

=> Sum of the roots = α + β = -(-7) = 7,

=> Product of the roots = αxβ = (9/1) = 9,

3. The value α-β can be also written as,

=> (α-β)² = α² + β² + 2αβ - 4αβ,

=> (α-β)² = (α + β)² - 4αβ,

=> (α-β) = √((α + β)² - 4αβ), (Consider as equation 1)

4. Substitute the values of α + β and αβ in equation 1,

=> (α-β) = √[(7)² - 4(9)],

=> (α-β) = √(49-36),

=> (α-β) = √(13).

Therefore, the value of α-β is √(13).