SATHEE: Theory of Equations 1 Question 24

Theory of Equations 1 Question 24

25. If one root is square of the other root of the equation $x^{2} + p x + q = 0$ , then the relation between $p$ and $q$ is

(a) $p^{3} - q (3 p - 1) + q^{2} = 0$

(2004, 1M)

(b) $p^{3} - q (3 p + 1) + q^{2} = 0$

(d) $p^{3} + q (3 p + 1) + q^{2} = 0$

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Answer:

Correct Answer: 25. (a)

Solution:

Let the roots of $x^{2} + p x + q = 0$ be $α$ and $α^{2}$ .

$\begin{array}{cc} \Rightarrow & α + α^{2} = - p and α^{3} = q \\ \Rightarrow & α (α + 1) = - p \\ \Rightarrow & α^{3} α^{3} + 1 + 3 α (α + 1) = - p^{3} [cubing both sides] \\ \Rightarrow & q (q + 1 - 3 p) = - p^{3} \\ \Rightarrow & p^{3} - (3 p - 1) q + q^{2} = 0 \end{array}$

Theory of Equations 1 Question 24

25. If one root is square of the other root of the equation $x^{2} + p x + q = 0$ , then the relation between $p$ and $q$ is

Answer:

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Theory of Equations 1 Question 24

25. If one root is square of the other root of the equation x2+px+q=0, then the relation between p and q is

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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25. If one root is square of the other root of the equation $x^{2} + p x + q = 0$ , then the relation between $p$ and $q$ is