Question

Fing the zeroes of 4x²- 7 and verify the relationship between the its coefficient

Answer 1

Answer:

$4 {x}^{2} - 7 = 0$

Given equation is $4 {x}^{2} - 7$Equate this equation with zero

$4 {x}^{2} - 7 = 0$

${( \sqrt{</strong><strong>4</strong><strong>}x) }^{2} - { (\sqrt{7} )}^{2} = 0$$( \sqrt{</strong><strong>4</strong><strong>}x + \sqrt{7} )( \sqrt{2 }x - \sqrt{7}</strong> ) <strong>= 0$

$x = \frac{ - \sqrt{7} }{ \sqrt{4} }$

OR

$x = \frac{ \sqrt{7} }{ \sqrt{4} }$

☑ If we compare the equation with ax^2 + bx + c = 0 then a , b, c are the coefficients of the equation

Therefor consider the zeros as alpha and beta

α = - √7/ √4 = -√7 / 2

β = √7 / √ 4 = √7 / 2

☑α + β = - b / a

⟹ α + β = - b / a

⟹ -b / a = (-√7 / 2) +( √7 /2 )

= (- √7 + √7 ) / 2

= 0 / 2= 0

And

☑ α x β = c / a

⟹α x β = c / a

=( -√7 / 2 ) (√7 / 2 )

= - 7 / 4