Question

Identify the nature of root of x square - 3 x + 4 root 2 is equal to zero

Answer 1

Answer:

imaginary roots

Step-by-step explanation:

The given quadratic equation

x²-3x+4√2 = 0

on comparing ax²+bx+c

a= 1, b = -3 , c = 4√2

thus, b²-4ac = (-3)²-4×1×4√2

= 9-16√2

= 9 - 16×1.414

= 9 - 22.624 = - 13.624 ( a negative no)

=> b²- 4ac < 0

=> the roots of the given quadratic equation

are imaginary.

Answer 2

Answer:

Nature of roots of the given equation is imaginary.

Step-by-step explanation:

Given equation is ${x}^{2} - 3x + 4 = 0........(1)$

We are comparing equation (1) with equation

$a {x}^{2} + bx + c = 0$

Where a is coefficient of ${x}^{2}$

and b is coefficient of x and c is constant.

After comparison we get,

$a = 1 \\ b = - 3 \\ c = 4$

Now we need to find value of ${b}^{2} - 4ac$

So,

${b}^{2} - 4ac = {( - 3)}^{2} - 4 \times 1 \times 4 = 9 - 16 = - 7$

We know,

If ${b}^{2} - 4ac = 0$

then roots of the equation are equal.

If ${b}^{2} - 4ac < 0$

the roots of the equation are imaginary.

and if ${b}^{2} - 4ac > 0$

then roots of the equation are unequal.

So roots of equation (1) are imaginary.