Show that x2 + 4x + 7 has no zero.
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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.
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