Question

Find the zero of polynomial
4√5 – 24x
9√5 and the
relations between the
the coefficents of polynomials

Answer 1

Step-by-step explanation:

Given -

• p(x) = 4√5x² - 24x - 9√5

To Find -

• Zeroes of the polynomial
• Verify the relationship between the zeroes and the coefficient

Now,

→ 4√5x² - 24x - 9√5

Here,

a = 4√5

b = -24

c = -9√5

By using quadratic formula :-

• → x = -b ± √b² - 4ac/2a

→ -(-24) ± √(-24)² - 4×4√5×-9√5/2(4√5)

→ 24 ± √576 + 720/8√5

→ 24 ± √1296/8√5

→ 24 ± 36/8√5

Zeroes are -

x = 24 + 36/8√5

→ 60/8√5

→ 15/2√5

And

x = 24 - 36/8√5

→ -12/8√5

→ -3/2√5

Verification :-

• α + β = -b/a

→ 15/2√5 + (-3/2√5) = -(-24)/4√5

→ 15 - 3/2√5 = 24/4√5

→ 12/2√5 = 6/√5

→ 6/√5 = 6/√5

LHS = RHS

And

• αβ = c/a

→ 15/2√5 × -3/2√5 = -9√5/4√5

→ -45/20 = -9/4

→ -9/4 = -9/4

LHS = RHS

Hence,

Verified...

It shows that our answer is absolutely correct.

Answer 2

${\huge{\underbrace{\overbrace{\red{Answer:-}}}}}$

$\implies$ 15/2√5

$\implies$ -3/2√5

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

• p(x) => 4√5 – 24x 9√5

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

• zeros of the polynomial.
• verify the relationship between the zeros of the coefficient.

Now,

$\implies$ 4√5 – 24x 9√5

$\implies$ a = 4√5

$\implies$ b = -24

$\implies$ c = -9√5

By using quadratic formula:

$\implies$ x = -b +,- √b² - 4ac/2a

$\implies$ -(-24) -,+ √(-24)² - 4 × 4√5 × (-9√5/2)(4√5)

$\implies$ 24 -,+ √576 + 720/8√5

$\implies$ 24 +,- √1296/8√5

$\implies$ 24 +,- 36/8√5

$\implies$ x = 24 + 36/8√5

$\implies$ 60/8√5

$\implies$ 15/2√5

$\implies$ x = 24 + 36/8√5

$\implies$ -12/8√5

$\implies$ -3/2√5

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

• β + α = -b/a

$\implies$ 15/2√5 + (-3/2√5) = -(-24)/4√5

$\implies$ 15 - 3/2√5 = 24/4√5

$\implies$ 12/2√5 = 6/√5

$\implies$ 6/√5 = 6/√5

$\large\underline\mathrm{LHS \: = \: RHS}$

• βα = c/a

$\implies$ 15/2√5 × -3/2√5 = -9√5/4√5

$\implies$ -45/20 = -9/4

$\implies$ -9/4 = -9/4

$\large\underline\mathrm{LHS \: = \: RHS}$

$\large\underline\mathrm{This \: answer \: is \: correct.}$

${\huge{\underbrace{\overbrace{\red{hope \: it \: helps \: you \: plz \: mark \: me \: brainlist \: .-}}}}}$