SATHEE: Matrices and Determinants 1 Question 15

Matrices and Determinants 1 Question 15

15. Let $b = 6$ , with $a$ and $c$ satisfying Eq. (i). If $α$ and $β$ are the roots of the quadratic equation $a x^{2} + b x + c = 0$ , then $\sum_{n = 0}^{\infty} (\frac{1}{α} + \frac{1}{β})^{n}$ is equal to

(a) 6

(b) 7

(d) $\infty$

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Answer:

Correct Answer: 15. (b)

Solution:

If $b = 6 \Rightarrow a = 1$ and $c = - 7$

$∴ a x^{2} + b x + c = 0 \Rightarrow x^{2} + 6 x - 7 = 0$

$\Rightarrow (x + 7) (x - 1) = 0$

$∴ x = 1, - 7$

$\begin{aligned} \Rightarrow \sum_{n = 0}^{\infty} (\frac{1}{1} - \frac{1}{7})^{n} & = 1 + \frac{6}{7} + {\frac{6}{7}}^{2} + \dots + \infty = \frac{1}{1 - \frac{6}{7}} & = \frac{1}{1 / 7} = 7 \end{aligned}$

Matrices and Determinants 1 Question 15

15. Let $b = 6$ , with $a$ and $c$ satisfying Eq. (i). If $α$ and $β$ are the roots of the quadratic equation $a x^{2} + b x + c = 0$ , then $\sum_{n = 0}^{\infty} (\frac{1}{α} + \frac{1}{β})^{n}$ is equal to

Answer:

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Matrices and Determinants 1 Question 15

15. Let b=6, with a and c satisfying Eq. (i). If α and β are the roots of the quadratic equation ax2+bx+c=0, then ∑n=0∞(1α+1β)n is equal to

Answer:

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15. Let $b = 6$ , with $a$ and $c$ satisfying Eq. (i). If $α$ and $β$ are the roots of the quadratic equation $a x^{2} + b x + c = 0$ , then $\sum_{n = 0}^{\infty} (\frac{1}{α} + \frac{1}{β})^{n}$ is equal to