Question

If the difference between the roots of equation x2 + px + 8 = 0 is 2 , then p is equal to ......


Please give detailed solution of this answer......

Answer 1

♧♧HERE IS YOUR ANSWER♧♧

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.

♧♧HOPE THIS HELPS YOU♧♧

Answer 2

Answer:

The correct answer is $&p=\pm 6$.

Step-by-step explanation:

Let the quadratic equation be,

$\mathrm{ax}^{2}+\mathrm{bx}+c=0$

Given:

If the difference between the roots of the equation $\mathrm{x}^{2}+\mathrm{px}+8=0$ is 2

To find the value of p.

Step 1

Let $a$ and $b$ are the roots of the given equation. Then,

$&a+b=-p$

Consider, $&a b=8$

and $&a-b=2$

then the square root of

$&(a-b)^{2}=4$

(A binomial expansion exists as a technique used to allow us to expand and simplify algebraic expressions in the form into a totality of terms of the form.

The binomial theorem specifies the expansion of any power $(a+b)^{m}$of a binomial $(a+b)$ as a certain sum of products $a^{i} b^{j}$, such as

$(a+b)^{2}=a^{2}+2 a b+b^{2} \text {. }$)

Step 2

$&(a+b)^{2}-4 a b=4$

Substituting the values $(a+b)$ and $ab$, then

$&p^{2}-32=4$

$&p^{2}=36$

$&p=\pm 6$

Therefore, the correct answer is $&p=\pm 6$.

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