Question

2x^2 + x + 4 = 0
plz help me in this question......

Answer 1

Answer:

It has no real roots.

It's imaginary roots are [ -1 ± √ -31 ] / 4

Step-by-step explanation:

2x^2 + x + 4 = 0

It is of the form ax^2 + bc + c = 0

Where

a = 2, b = 1, c = 4

Thus,

x = [ -b ± √ ( b^2 - 4ac ) ] / 2a

x = [ -1 ± √ { 1^2 - 4 ( 2 ) ( 4 ) } ] / 2 ( 2 )

x = [ -1 ± √ { 1 - 32} ] / 4

x = [ -1 ± √ -31 ] / 4

But, -31 is a negative number.

Thus, √ -31 is a non real number.

Hence, the given quadratic equation has no real roots.

P. S. It's imaginary root are [ -1 ± √ -31 ] / 4

Note:

For any quadratic equation,

If b^2 - 4ac > 0, it has real and distinct roots.

If b^2 - 4ac = 0, it has real and equal roots.

If b^2 - 4ac < 0, it has no real roots.

This may be used to find the nature of the roots and to confirm whether they are real or no.

Answer 2

as you can see -31 comes inside underroot.
so we can infer as the discriminant(b²-4ac) is negative this equation has no real roots but rather imaginary root.
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