Question

2x² + 5root3x + 6 solve this by using qudratic formula

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Answer 1

Step-by-step explanation:

Given -

• p(x) = 2x² + 5√3x + 6

To Find -

• Zeroes of polynomial by using quadratic formula

As we know that :-

• x = -b ± √b² - 4ac/2a

⇝2x² + 5√3x + 6

here,

a = 2

b = 5√3

c = 6

Now,

⇝-(5√3) ± √(5√3)² - 4× (2) × (6)/2(2)

⇝-5√3 ± √75 - 48/4

⇝-5√3 ± √27/4

⇝-5√3 ± 3√3/4

Zeroes are -

x = -5√3 + 3√3/4

⇝-2√3/4

⇝-√3/2

And

x = -5√3 - 3√3/4

⇝-8√3/4

⇝-2√3

Hence,

Zeroes of the given polynomial are -√3/2 and -2√3

Verification :-

• α + β = -b/a

⇝-√3/2 + -2√3 = -5√3/2

⇝-√3 - 4√3/2 = -5√3/2

⇝-5√3/2 = -5√3/2

LHS = RHS

And

• αβ = c/a

⇝-√3/2 × -2√3 = 6/2

⇝3 = 3

LHS = RHS

Hence,

Verified...

It shows that our answer is absolutely correct.