Question

write the Quadratic equation whose roots are 4+√5 and 4-√5​

Answer 1

Step-by-step explanation:

we have fomula of equation when we have roots:

Formula: x^2- (sum of roots) x + (product of roots)..............1

Now,

1) sum of roots = (4+√5)+(4-√5) = 4+4. {√5-√5=0}

=8...........................2.

2) product of roots = (4+√5)(4-√5)

= ( square of 4)-( square of √5) = 16 - 5 = 11......................3

therefore,put 2nd and 3rd in 1st

x^2 - 8x + 11...............quadratic equation.

Answer 2

Answer:

x² - 2√5 - 11

Step-by-step explanation:

It is given that √5 - 4 and √5 + 4 are the zeroes of the required polynomial.

Let the two zeroes be α and β of the required polynomial.

∴ α = √5 - 4, β = √5 + 4

_____________________________

Now,

• Sum of zeroes = α + β

→ (√5 - 4) + (√5 + 4)

→ √5 - 4 + √5 + 4

→ √5 + √5

→ 2√5

• Product of zeroes = αβ

→ (√5 - 4)(√5 + 4)

Identity : (a - b)(a + b) = a² - b²

Here, a = √5, b = 4

→ (√5)² - (4)²

→ 5 - 16

→ - 11