Question

i) 5x2 - 6V5 x + 9 = 0. discuss the nature of roots. if real root exist, find them​

Answer 1

Answer:

roots are real ;   3√5 / 5 - roots

Step-by-step explanation:

Discriminant tells whether an eq. has real roots, complex, so on.

Here,

  Discriminant = ( 6√5 )² - 4( 5 * 9 )

⇒ ( 36 * 5 ) - 4( 45 )

⇒ ( 180 ) - 180

⇒ 0

       As discriminant is 0, roots are real and equal.

so, using quadratic formula :

⇒ x = ( - b ± √D ) / 2(5)

      = [ - ( - 6√5 ) ± √0 ] / 2(5)

      = [ 6√5 ± 0 ] / 10

      = 6√5 / 10

       = 3√5 / 5

Answer 2

5x² -6√5x + 9 = 0

Here:-

a=5, b= -6√5 and c=9

To find the nature of roots:-

D= b²-4ac

D= (-6√5)² - 4×5×9

D= 36×5 - 180

D= 180-180=0

When D= 0, this shows that there exists two equal roots for equation 5x² -6√5x + 9 = 0

The equal roots are shown by -b/2a and -b/2a

Equal roots= -(-6√5)/2×9 & -(-6√5)/2×9

Equal roots= 6√5/18 & 6√5/18

Equal roots= √5/3 and √5/3