Question

If α and ß are roots of equations 2x ^ 2 - 4x - 3 = 0 . Find the value of α+ ß and αß​

Answer 1

The value of

α+β = -2

αβ = -3/2

Explanation:

Given Equation:

2x ² - 4x - 3 = 0

To find:

α+β and αβ

We know the formula for α and β

FORMULA:

α  =  $\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

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

To find α+β ,

α+β = $\frac{-b+\sqrt{b^{2}-4ac } }{2a}$ + $\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

Taking   $\frac{1}{2a}$ as common,

α+β = $\frac{1}{2a}( -b+\sqrt{b^{2}-4ac )$ + $-b-\sqrt{b^{2}-4ac$

α+β = $\frac{1}{2a}( -b)+(-b)$

α+β = $\frac{1}{2a}( -2b)$

α+β = $\frac{-b}{a}$

to find  αβ,

αβ = $(\frac{-b+\sqrt{b^{2}-4ac } }{2a})$  $(\frac{-b-\sqrt{b^{2}-4ac } }{2a})$

αβ = $\frac{b^{2} -({b^{2}-4ac } )}{4a^{2} }$  

αβ = $\frac{b^{2} -{b^{2}+4ac } }{4a^{2} }$  

αβ = $\frac{{4ac } }{4a^{2} }$  

αβ = $\frac{{c } }{a} }$  

From the equation,

a = coefficient of x²

b = coefficeint of x

c = constant

a = 2

b = 4

c  = -3

Applying thess values in the formula,

α+β = $\frac{-b}{a}$

α+β = $\frac{-4}{2}$

α+β = -2

αβ = $\frac{{c } }{a} }$  

αβ = $\frac{{-3 } }{2} }$  

The value of α+ β and αβ is  -2, -3/2