Question

Show that x2 + 4x + 7 has no zero.​

Answer 1

Answer:

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Answer 2

Answer :-

x² + 4x + 7 has no zero.

Step-by-step explanation :-

Given :

p(x) = x² + 4x + 7

To find :

To show that the above equation has non zero.

Solution :

x² + 4x + 7

x² + 4x + [(4) + 3]

x² + 2(x)(2) + 2² + 3

∵ (a + b)² = a² + b² + 2ab

∴ p(x) = (x + 2)² + 3

If we take any value in x, it will be positive, so p(x) cannot be zero,

∴ x² + 4x + 7 has no zero.

or

x² + 4x + 7

Comparing it to b² - 4ac (Discriminant)

a = 1, b = 4, c = 7

4² - 4(1)(7)

16 - 28

-12 > 0.

∴ If discriminant is negative and it is greater than 0, so the roots are imaginary and they have no zeroes.

If Discriminant > 0, two real solutions.

if Discriminant = 0, one real solution.

If Discriminant < 0, two imaginary solutions.