Question

alpha and beta are the zeros of the polynomial 2 x square - 4 x + 5 find the value of bracket Alpha minus beta whole square ​

Answer 1

ANSWER:

• Value of (α-β)² is (-6)

GIVEN:

• α and β are the Zeros of the quadratic polynomial 2x²-4x+5.

TO FIND:

• (α-β)²

SOLUTION:

Formula

=> (α+β) = -(coefficient of x)/coefficient of x²

=> αβ = Constant term/coefficient of x²

=> (α-β)² = (α+β)²-4αβ ....(i)

P(x) = 2x²-4x+5

=> α+β = -(-4)/2

=> α+β = 2

=>αβ = 5/2

Putting these value in eq(i) we get;

=> (α-β)²= (2)²-4(5/2)

=> (α-β)²= 4-10

=> (α-β)²= (-6)

Value of (α-β)² is (-6)

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab

Answer 2

GIVEN:

α and β are the two zeroes of polynomial 2x² - 4x + 5

TO FIND:

The value of (α-β)²

SOLUTION:

We know that,

Sum of zeroes of polynomial = α + β = -b/a

Product of zeroes = αβ = c/a

(a - b)² = (a + b)² - 4ab

In the above polynomial,

a = 2 ; b = -4 and c = 5

Now,

Sum of zeroes = α + β = -(-4)/2 = 1

Product of zeroes = αβ = 5/2

(α - β)² = (α + β)² - 4αβ

= (2)² - 4(5/2)

= 4 - 10

= -6

Therefore, the value of (α - β)² is -6.