Question

Assertion :The polynomial $x^4+4x^2+5$ has four real zeroes. Reason: If p(x) is divided by (x-k), then the remainder $=$ p(k)

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

Assertion:
Let $p\left(x\right)=x^4+4x^2+5$
To finD zeroes of $p\left(x\right)$, we consider
$p\left(x\right)=0$
$\Rightarrow x^4+4x^2+5=0$
$\Rightarrow x^4+4x^2+4+1=0$
$\Rightarrow (x^2+1{)}^2=-1$
Which is not possible. Therefore, the given polynomial has no zero.
Reason:
It is true my remainder theorem.
Hence option D is correct.