Question

The equation 2x2 + 3x + 1 = 0 has
O a) An irrational roots
O b) No irrational roots
O c) Two irrational roots
d) Complex Roots​

Answer 1

Given:

• A quadratic equⁿ is given to us .
• The equⁿ is 2x² + 3x + 1 = 0.

To Find:

• The correct option between them.

1. a) An irrational roots
2. b) No irrational roots
3. c) Two irrational roots
4. d) Complex Roots.

Answer:

We can determine the nature of roots by finding the Discriminant of the quadratic equation.

Now of a standard quadratic equation in ax²+bx+c form , the discriminant is given by b²-4ac .

With respect to Standard form ,

Here

• a = 2
• b = 3
• c = 1

=> D = b²-4ac.

=> D = (3)² - 4×2×1.

=> D = 9-8.

=> D = 1.

Hence the discriminant is positive (D>0) , so we can say that the roots are real.

=> x = -b±√b²-4ac/2a

=> x = -3± 1/2×2.

=> x = -3±1/4.

=> x = -3+1/2,-3-1/2

=> x = -2/2,-4/2

=> x = -1,-2.

Hence there are real roots which implies that there are no irrational roots.

Hence the correct option is (b) No Irrational roots.