Question

if the absolute difference between two roots of x^2 +px+3 = 0 is root p then p =​

Answer 1

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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.

Answer 2

Answer:

the real answer is "-3&4"

Step-by-step explanation:

given that:

let the roots of the equation be x and y.....

x+y= -p.........(I)

xy= 3.............(ii)

A/C to question,

x-y= √p

squaring both side we get,

(x-y)²= p

by solving it,

(x+y)²-4xy = p

(-p)²-4(3)=p

p²-p-12=0

(p+3)(p-4)=0

so, the value of p is equal to -3 & 4.......

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