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Polynomials — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsPolynomials1 Mark
MCQ
Let $f(x)$ be a polynomial such that $\text{f}\Big(-\frac{1}{2}\Big)=0,$ then a factor of $f(x)$ is:
  • A
    $2x - 1$
  • ✓
    $2x + 1$
  • C
    $x - 1$
  • D
    $x + 1$
✓

Answer

Correct option: B.
$2x + 1$
If $f(x)$ is a polynomial and $\text{f}(\alpha)=0.$ Then $(\text{x}-\alpha)$ is a factor of $f(x)$ or vice versa if $(\text{x}-\alpha)$ is a factor of $f(x)$ then $\text{f}(\alpha)=0.$
Now,
$\text{f}\Big(\frac{-1}{2}\Big)=0$
So, at $\text{x}=\frac{-1}{2},\text{f(x)}=0$
Or at $2x = -1, f(x) = 0$
Or at $2x + 1 = 0, f(x) = 0$
$⇒ (2x + 1)$ is a factor of $f(x).$

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