Question

let a and be the zeroes of the polynomial 2x²+3x-6 find the value of : a-b

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Answer 1

Answer:

the given equation is:

2x ^2+3x-6=0

Comparing the above equation by using the quadratic formula the zeros of the above are{-b+ or -√(b^2–4ac)}/2a

= {-3 + or - √(9 - 4×2×(-6))}/2×2= {-3 + or - √57}/4. So, the zeros are (-3 + √57)/4, (-3 - √57)/4

Step-by-step explanation:

hope it's helps you

Answer 2

Answer :

√57/2

Explanation :

Given polynomial,

⇒2x² + 3x - 6

On comparing with ax² + bx + c

We get,

• a = 2
• b = 3
• c = -6

Then,

• α + β = -b/a = -3/2
• αβ = c/a = -6/2 = -3

Using identity,

⇒ (α - β)² = (α + β)² - 4αβ

Substituting the values,

⇒ (α - β)² = (-3/2)² - 4(-3)

⇒ (α - β)² = 9/4 + 12

⇒ (α - β)² = 9 + 48/4

⇒ α - β = √(57/4)

⇒ α - β = √57/√4

⇒ α - β = √57/2

Required answer : √57/2