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

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Answer:

Correct Answer: 37. (b)

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.

Theory of Equations 1 Question 36

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

Answer:

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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 ax2+bx+c=0

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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