Question

the roots of a quadratic equation x2 - px + 4 = 0 are equal then p = ?​

Answer 1

Answer:

± 4.

Step-by-step explanation:

Given :

p ( x ) = x² - p x + 4

We know for equals roots :

b² - 4 a c = 0

( - p )² - 4 × 1 × 4 = 0

p² - 16 = 0

p² = 16

p = √ 16

p = ± 4 .

Therefore , the value of p is ± 4.

Answer 2

Step-by-step explanation:

Given equation :

x² + px + 8 = 0 .....(i)

Let, α and β are roots of (i).

Then,

α + β = - p .....(ii)

and

αβ = 8 .....(iii)

Given :

α - β = 2

=> (α - β)² = 2²

=> (α + β)² - 4αβ = 4

=> p² - (4 × 8) = 4

=> p² - 32 = 4

=> p² = 32 + 4 = 36 = 6²

=> p = ± 6

So, the required values of p are

p = ± 6.