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Quantitative Aptitude

Functions

Let fx be a q...

Question

Let $f (x)$ be a quadratic polynomial such that $f (- 1) + f (2) = 0$ . If one of the roots of $f (x) = 0$ is $3,$ then its other root lies in:

(0, 1)

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(1, 3)

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(- 1, 0)

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(- 3, - 1)

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Solution

The correct option is C $(- 1, 0)$
Let $f (x) = a (x - 3) (x - α)$
$f (- 1) + f (2) = 0$
$a [(- 1 - 3) (- 1 - α) + (2 - 3) (2 - α)] = 0$
$a [4 + 4 α - 2 + α] = 0$
$5 α + 2 = 0$
$\Rightarrow α = - \frac{2}{5}$

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Let f(x) be a quadratic polynomial such that f(−1)+f(2)=0. If one of the roots of f(x)=0 is 3, then its other root lies in:

The correct option is C (−1,0)Let f(x)=a(x−3) (x−α) f(−1)+f(2)=0 a[(−1−3) (−1−α)+(2−3) (2−α)]=0 a[4+4α−2+α]=0 5α+2=0 ⇒α=−25

Let $f (x)$ be a quadratic polynomial such that $f (- 1) + f (2) = 0$ . If one of the roots of $f (x) = 0$ is $3,$ then its other root lies in:

The correct option is C $(- 1, 0)$
Let $f (x) = a (x - 3) (x - α)$
$f (- 1) + f (2) = 0$
$a [(- 1 - 3) (- 1 - α) + (2 - 3) (2 - α)] = 0$
$a [4 + 4 α - 2 + α] = 0$
$5 α + 2 = 0$
$\Rightarrow α = - \frac{2}{5}$