Class 8 question

Question

Find the value of x using quadratic formula
16x^4- 28x² - 8=0

Answer 1

Substitute x² with t

16 x⁴ - 28 x² - 8 = 0

become

16 t² - 28 t - 8 = 0

Divide both sides by 4

4 t² - 7 t - 2 = 0

The coefficients are:

a = 4 , b = - 7 , c = - 2

t1/2 = [ - b ± √ ( b² - 4 a c ) ] / 2 a =

[ - ( - 7 ) ± √ ( ( - 7 )² - 4 ∙ 4 ∙ ( - 2 ) ) ] / 2 ∙ 4 =

[ 7 ± √ ( 49 + 32 ) ] / 8 = ( 7 ± √81 ) / 8 = ( 7 ± 9 ) / 8

t1 = ( 7 + 9 ) / 8 = 16 / 8 = 2

t2 = ( 7 - 9 ) / 8 = - 2 / 8 = - 1 / 4

If x² = t

then

x = ± √ t

t1 = 2

x = ± √2

t2 = - 1 / 4

x = ± √ -1 / √4 = ± i / 2

The solutions are:

x = - i / 2 , x = i / 2 , x = -√2 , x = -√2

Answer 2

The solutions are:

x = - i / 2 , x = i / 2 , x = -√2 , x = √2