Question

Find roots of 2x^2 + 5root 3x +6 =0 by quadratic formula

Answer 1

Step-by-step explanation:

Given -

• p(x)= 2x² + 5√3x + 6 = 0

To Find -

• Zeroes of the polynomial

By using quadratic formula :-

• x = -b ± √b² - 4ac/2a

here,

a = 2

b = 5√3

c = 6

Now,

→ x = -(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

→ -8√3/4

→ -2√3

And

→ x = -5√3 + 3√3/4

→ -2√3/4

→ -√3/2

Hence,

The zeroes are -2√3 and -√3/2.

Verification :-

As we know that :-

• α + β = -b/a

→ -2√3 + (-√3/2) = -(5√3)/2

→ -2√3 - √3/2 = -5√3/2

→ -4√3 - √3/2 = -5√3/2

→ -5√3/2 = -5√3/2

LHS = RHS

And

• αβ = c/a

→ -2√3 × -√3/2 = 6/2

→ 3 = 3

LHS = RHS

Hence,

Verified..

Formula Used :-

☞ Quadratic formula :

• x = -b ± √b² - 4ac/2a

Answer 2

$\large{\boxed{\underline{\underline{\bf{\red{Answer:-}}}}}}$

$\implies$ -√3/2

$\implies$ -2√3

$\large\underline\mathrm{Given:-}$

• p(x) = 2x² + 5√3x + 6 = 0

$\large\underline\mathrm{To \: find}$

• zeroes of the polynomial

by using the formula in quadratic polynomial.

• x => -b +,- √b² - 4ac/2a

$\implies$ a = 2

$\implies$ b = 5√3

$\implies$ c = 6

$\large\underline\mathrm{now,}$

$\implies$ x =-(5√3) +,- √(5√3(² - 4 × 2 × 6/2(2)

$\implies$ -5√3 -,+ √75 - 48/4

$\implies$ -5√3 +,- √27/4

$\implies$ -5√3 +,- 3√3/4

$\implies$ -5√3 + 3√3/4

$\implies$ -8√3/4

$\implies$ -2√3

$\implies$ -5√3 - 3√3/4

$\implies$ -2√3/4

$\implies$ -√3/2

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$