Question

If alpha and beta are the zeros of the quadratic polynomial f of x = 6X square + X - 2 find the value of Alpha by beta + beta by Alpha

Answer 1

Step-by-step explanation:

your answer is above attachment

Answer 2

Given data : If α and β are the zeros of the quadratic polynomial f(x) = 6x² + x − 2.

To find : The value of α/β + β/α.

Solution :

Now,

⟹ 6x² + x - 2 = 0

compair above quadratic equation with ax² + bx + c = 0

Hence,

⟹ a = 6, b = 1 and c = - 2

According to given data, we know that α and β are the zeros of the quadratic polynomial.

Now,

⟹ α + β = - b/a

⟹ α + β = - 1/6

and

⟹ αβ = c/a

⟹ αβ = - 2/6

⟹ αβ = - 1/3

Now,

⟹ α/β + β/α

= (α * α)/(β * α) + (β * β)/(α * β)

= α²/αβ + β²/(- 1/3)

= (α² + β²)/(- 1/3)

= (α + β)² - 2αβ/(- 1/3)

= {(1/6)² + 2 * 1/3}/(- 1/3)

= {(1/6)² + 2 * 1/3}/(- 1/3)

= {1/36 + 2/3}/(- 1/3)

= {1/36 + 24/36}/(- 1/3)

= {1 + 24/36}/(- 1/3)

= {25/36}/(- 1/3)

= 25/36 * - 3/1

= - 75/36

= - 25/12

Answer : α/β + β/α = - 25/12