Question

Please help me out to know the answer.

Explantion also please

Answer 1

Answer:(d) is right answer

Step-by-step explanation:

Answer 2

Answer:

p ≈ 10.4336

or

p ≈ -0.08

Step-by-step explanation:

The given equation is

x² - px + 36 = 0

Comparing the equation with general form

ax² + bx + c = 0

we get

a = 1    ,   b = -p  and  c = 36

If α and β roots of equation then

sum of roots of equation = α + β = -b/a

Putting the values we get

α + β = -(-p)/1 = p

Products of roots = αβ = c/a

Putting the values we get

αβ = 36/1 = 36

Now

We are given that

α³ + β³ = 9

Using the formula a³ + b³ = (a + b)(a² - ab + b²) we get

(α + β)(α² - αβ + β²) = 9

using α² + β² = (α + β)² - 2αβ we get

(α + β)( - αβ + (α + β)² - 2αβ ) = 9

(α + β)( (α + β)² - 3αβ ) = 9

Putting the values of sum and product on left side we get

( p )( (p² - 3(36) ) = 9

p³ - 108p = 9

p³ - 108p = 9

p3 - 108p - 9 = 0

If we solve it with the help of graph we get

p ≈ 10.4336

or

p ≈ -0.08