Question

EXERCISE - 5.4
Find the nature of the roots of the following quadratic equations. If real roots exist, find
them:
(1) 2x² – 3x+5=0
(i) 3x² - 413x+4 = 0
(i) 2x² - 6x + 3 = 0​

Answer 1

Step-by-step explanation:

Discriminant value=b²-4ac.

(1) 2x² – 3x+5=0

here a=2, b=-3, c=5

b²-4ac=(-3)²-4(2)(5)

=>9-40

=>-31<0

The equation has no real roots.

(i) 3x² - 13x+4 = 0

here a=3, b=-13, c=4.

b²-4ac=(-13)²-4(3)(4)

=>169-48

=>121>0

The equation has distint and real roots.

(i) 2x² - 6x + 3 = 0

here a=2, b=-6, c=3

b²-4ac=(-6)²-4(3)(2)

=>36-24

=>12>0

The equation has distinct and real roots.