SATHEE: Theory of Equations 1 Question 36

Theory of Equations 1 Question 36

37. Let $a > 0, b > 0$ and $c > 0$ . Then, both the roots of the equation $a x^{2} + b x + c = 0$

(1979, 1M)

(a) are real and negative

(b) have negative real parts

(d) None of the above

Assertion and Reason

For the following question, choose the correct answer from the codes (a), (b), (c) and (d) defined as follows :

(a) Statement I is true, Statement II is also true; Statement II is the correct explanation of Statement I

(b) Statement I is true, Statement II is also true; Statement II is not the correct explanation of Statement I

(d) Statement I is false; Statement II is true

Show Answer

Solution:

Since, $a, b, c > 0$ and $a x^{2} + b x + c = 0$

$\Rightarrow x = \frac{- b}{2 a} \pm \frac{\sqrt{b^{2} - 4 a c}}{2 a}$

Case I When $b^{2} - 4 a c > 0$

$\Rightarrow x = \frac{- b}{2 a} - \frac{\sqrt{b^{2} - 4 a c}}{2 a}$

and $\frac{- b}{2 a} + \frac{\sqrt{b^{2} - 4 a c}}{2 a}$ both roots, are negative.

Case II When $b^{2} - 4 a c = 0$

$\Rightarrow x = \frac{- b}{2 a}$ , i.e. both roots are equal and negative

Case III When $b^{2} - 4 a c < 0$

$\Rightarrow x = \frac{- b}{2 a} \pm i \frac{\sqrt{4 a c - b^{2}}}{2 a}$

have negative real part.

$∴$ From above discussion, both roots have negative real parts.

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Theory of Equations 1 Question 36

37. Let $a > 0, b > 0$ and $c > 0$ . Then, both the roots of the equation $a x^{2} + b x + c = 0$

Assertion and Reason

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Theory of Equations 1 Question 36

37. Let a>0,b>0 and c>0. Then, both the roots of the equation ax2+bx+c=0

Assertion and Reason

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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37. Let $a > 0, b > 0$ and $c > 0$ . Then, both the roots of the equation $a x^{2} + b x + c = 0$