Question

5. Find the nature of quadratic equation 4x²– 3x + 4
​

Answer 1

Answer:

answer for the given problem is given

Answer 2

Answer:

55 i²

Step-by-step explanation:

To understand the nature of the roots of a quadratic equation,

let us consider the general form a quadratic equation.

ax² + bx + c = 0

(Here a, b and c are real and rational numbers)

To know the nature of the roots of a quadratic-equation,

we will be using the discriminant

b² - 4ac.

Because b² - 4ac discriminates the nature of the roots.

Case 1 : b² - 4ac=0

The roots are real ,equal and rational

Case 2 : b² - 4ac>0 also real and perfect square

The roots are real, distinct and rational

Case 3 : b² - 4ac>0 but not a perfect square

The roots are real and irrational

Case 4 : b² - 4ac<0

The roots are imaginary

Case 5 : b² - 4ac≥0

The roots are real

Coming to the problem

4x²– 3x + 4 => b² - 4ac

(-3)²-4(4)(4)

=>9-64

=>-55

also written as. 55 i²

{ as we know that i=

$\sqrt{ - 1}$

SOBS

i²= -1 }

Now observing the cases and comparing the answer

Now observing the cases and comparing the answer

Now observing the cases and comparing the answer it belongs to case 4

Now observing the cases and comparing the answer it belongs to case 4 as -55<0

The nature of the roots is imaginary