Question

If α and β are zeroes of p(x)=3x²-2x-6, then find the value of (α-β)​

Answer 1

Answer:

GIVEN FUNCTION -

$p(x) = 3 {x}^{2} - 2x - 6$

IT HAVE TWO ROOTS -

$\alpha \: \: and \: \: \beta$

WE KNOW THAT DIFFERENCE OF ROOTS IS -

$\alpha - \beta = \frac{ \sqrt{d} }{a}$

$\alpha - \beta = \frac{ \sqrt{ {b}^{2} - 4ac } }{a}$

$\alpha - \beta = \frac{ \sqrt{ {( - 2) }^{2} - 4(3)( - 6) } }{3}$

$\alpha - \beta = \frac{ \sqrt{78} }{3}$

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