Question

if alpha and beta are the roots of the equation x^2-5x+6=0 then find (alpha - beta )

Answer 1

Answer:

$\alpha -\beta =-1 \: Or \: 1$

Step-by-step explanation:

$Given\:\alpha \: and \: \beta\\are \: roots \: of \: the \\equation \:x^{2}-5x+6=0$

Compare this equation with ax²+bx+c=0, we get

a = 1, b = -5, c = 6,

$Sum\:of \: the \: roots =\frac{-b}{a}$

$\implies \alpha+\beta=\frac{-(-5)}{1}=5$

$Product\:of\:the \:roots = \frac{c}{a}$

$\implies \alpha\beta=\frac{6}{1}=6$

$Now,\\(\alpha-\beta)^{2}=(\alpha+\beta)^{2}-4\alpha \beta$

$=5^{2}-4\times 6\\=25-24\\=1$

$\alpha -\beta =-1\: Or \: 1$

Therefore,

$\alpha -\beta =-1 \: Or \: 1$

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Answer 2

α - β = 1

Step-by-step explanation:

Given equation,

x^2 - 5x + 6 = 0

by comparing the given equation x^2 - 5x + 6 = 0 with ax^2 + bx + c = 0.

so, a = 1, b = -5, c = 6

As we know,

Sum of the roots = -b/a

⇒ α + β = -(-5)/1 = 5

The product of the roots = c/a

⇒ αβ = 6/1 = 6

Therefore, (α - β)^2 = (α + β)^2 - 4αβ

= 5^2 - 4 *6

= 25 - 24

= 1

∵ α - β = 1

Learn more: Roots of the equation

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