Question

If ∝ and ᵝ are zeroes of the polynomial x² -5x +k and ∝ - β = 1, then k is

Answer 1

Answer:

The value of k is 6....

In the equation,

x²-5x+k=0

$\alpha + \beta = 5 \\ \alpha \beta = k \\ \alpha - \beta = 1 \\ on \: solving \\ \ \ \alpha = 3 \\ \beta = 2 \\ so \: \alpha \beta = k \\ k = 6$

Step-by-step explanation:

Hope it helps you frnd......

Answer 2

✴ Given:

➠ ∝ and ᵝ are zeroes Of polynomial x² -5x +k

➠ ∝ - β = 1

✴ To find:

• Value of k

✴ Concept:

➳ Sum of zeroes is given by the formula

-b/a

where,

b is second term of polynomial i.e coeffecient if x

and a is first term i.e coffecient of x^2

➳ Product of zeroes is given by the formula

c/a

where,

c is last term of polynomial i.e constant term

and a is first term i.e coffecient of x^2

✴ Calculation:

Product of zeroes = c/a

⟶ ∝ × ᵝ = k/1

⟶ ∝ᵝ = k

∝ - ᵝ = 1 (given)

Squaring both sides we get,

⟶ ∝ ^2 + ᵝ^2 -2∝ᵝ = 1

as (a-b)^2 = a^2 + b^2 - 2ab

⟶ ∝ ^2 + ᵝ^2 -2k = 1

⟶ ∝ ^2 + ᵝ^2 = 1+2k

Further,

Sum of zeroes = -b/a

⟶ ∝ + ᵝ = -(-5)/1

⟶ ∝ + ᵝ = 5

Squaring both sides we get,

∝ ^2 + ᵝ^2 + 2∝ᵝ =25

as (a+b)^2 = a^2 + b^2 + 2ab

putting value of ∝ ^2 + ᵝ^2 from above equation,

⟶ ∝ ^2 + ᵝ^2 = 1+2k

⟶ ∝ ^2 + ᵝ^2 + 2∝ᵝ =25

⟶ 1+2k + 2k = 25

⟶ 1+4k = 25

⟶ 4k = 24

⟶ k = 6

✴ Answer:

k = 6