Question

Use the discriminant to determine the number of real roots the equation has. 3x2 – 5x + 1 =0​

Answer 1

Answer

The equation has 2 real and distinct roots .

Solution

We know that discriminant = b²-4ac .

The general form of quadratic equation is ax²+bx +c, So by comparing general form by the given quadratic equation we got :

ax² +bx +c = 3x²-5x +1 here ,

a = 3 ; b = -5 and c = 1 .

Now using the formula of discriminant:

b² - 4ac. = (-5)²-4(3)(1)

discriminant = 25 - 12

Discriminant = 13

Hence d >0

So, roots will be distinct and real

Answer 2

Given equation

3x^2 - 5x + 1= 0

Formula

D = b^2 - 4ac for equation ax^2 + bx + c

Given

a = 3

b= -5

c= 1

so

D = (-5)^2 - 4*3*1

D = 25 - 12

D = 13