Question

If α and β​ are the zeros of the quadratic polynomial f(x) = 6x^2 + x − 2, find the value of Alpha - Beta . Will mark brainliest for correct answer .

Answer 1

Hey there!

Equate the given equation to zero to find the our zeroes which is alpha and beta according to question

6 x^2 + x − 2 = 0

6 x^2 + 4 x − 3 x − 2 = 0

2 x (3 x + 2) − (3 x + 2)=0

by this , we get two equations:

• 2 x − 1= 0

• x = 1/2(alpha)

• 3 x + 2= 0

• x = −2/3(beta)

So, the value of α = 1/2 and β = -2/3

#Hope it helps!

Answer 2

Answer:

Given:

6x²+x-2=0

Solution:

$\alpha + \beta = \frac{ - 1}{6} \\ \alpha \beta = - \frac{2}{6} = - \frac{1}{3} \\ as \: the \: rule \\ {( \alpha + \beta )}^{2} =( { - \frac{1}{6} })^{2} \\ or \: {( \alpha - \beta )}^{2} + 4 \alpha \beta = \frac{1}{36} \\ or \: {( \alpha - \beta )}^{2} = \frac{1}{36} + \frac{4}{3} \\ or \: ( \alpha - \beta ) = \sqrt{ \frac{1 + 48}{36} } \\ or \: ( \alpha - \beta ) = \sqrt{ \frac{49}{36} } \\ finally \\ ( \alpha - \beta ) = \frac{7}{6}$

7/6 your answer.