Question

state the nature of the roots for the
quadratic equations x²+8x+8=0​

Answer 1

This could be better may be

Answer 2

we have to state the nature of the roots for the quadratic equation x² + 8x + 8 = 0

solution : 1st method : find Discriminant,

if D > 0 , then roots are real and distinct

if D = 0, then roots are real and equal

if D < 0, then roots are imaginary and distinct.

here, D = b² - 4ac = (8)² - 4 × 1 × 8

= 64 - 32 = 32 > 0

we see, D > 0 so roots are real and distinct.

2nd method : you can also find the nature of roots just by solving it.

x² + 8x + 8 = 0

⇒x² + 2 × x × 4 + (4)² - (4)² + 8 = 0

⇒[x² + 2 × x × 4 + (4)²] - 16 + 8 = 0

⇒(x + 4)² - 8 = 0

⇒(x + 4)² = 8

taking square root both sides we get,

⇒x + 4 = ± 2√2

⇒x = -4 ± 2√2

Therefore -4 - 2√2 and -4 + 2√2 are roots of given quadratic equation.

here we see, -4 - 2√2 and -4 + 2√2 are real and distinct.

Therefore roots of given quadratic are real and distinct.