Question

show that the polynomial x2 +2x+7 has no zeros​

Answer 1

heya

ANSWER:

p(x)=x²+2x+7

let us do the discriminant

d=b²-4ac

=2²-4(1)(7)

=4-28

=-24

as the discriminant is in negative

the roots are imaginary

so,the given polynomial has no roots

hope the answer helps u

Answer 2

Answer:

The polynomial $x^2 + 2x +7$ has no zeroes.

Step-by-step explanation:

Explanation:

Given in the question, $x^2 +2x +7$

As we know, a polynomial has no zeroes if $b^2 - 4ac < 0$.

• The "quadratic formula" is used to compute the solution for the two roots: The value  $b^2 -4ac$ determines the answer. The "discriminant" is the name for this concept.

Step 1:

By the use of the formula, $b^2 -4ac$ we can prove that the given polynomial has no zeroes if $b^2 -4ac < 0$

Now, from the question we have,

$x^2 + 2x +7$

a = 1 , b = 2 and c = 7

Where a, b, and c are the coefficients of $x^2 , x \ and c\ is \ constant$.

On putting the value in the formula we get.

⇒$(2)^2 - 4 (1)(7)$

⇒4 - 28

⇒-24 which is less than 0

So, here we can see that, $b^2 -4ac < 0$.

Final answer:

Hence, the polynomial $x^2 + 2x +7$ has no zeroes.

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