Class 10 Exam > Class 10 Questions > If the zeroes of the polynomial x ^ 2 + px + ...
Start Learning for Free
If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q?
Most Upvoted Answer
If the zeroes of the polynomial x ^ 2 + px + q are double in value to ...
Step 1: Identify the Roots of the Second Polynomial
To find the roots of the polynomial \(2x^2 - 5x - 3\), we can use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Here, \(a = 2\), \(b = -5\), and \(c = -3\).
Calculating the Discriminant
- \(b^2 - 4ac = (-5)^2 - 4(2)(-3) = 25 + 24 = 49\)
Finding the Roots
\[
x = \frac{5 \pm \sqrt{49}}{4} = \frac{5 \pm 7}{4}
\]
- Roots: \(x_1 = 3\), \(x_2 = -\frac{1}{2}\)
Step 2: Determine the Roots of the First Polynomial
Given that the roots of \(x^2 + px + q\) are double the roots of the second polynomial:
- New roots: \(2x_1 = 6\) and \(2x_2 = -1\)
Step 3: Formulate the Polynomial
The polynomial with roots \(6\) and \(-1\) can be expressed as:
\[
x^2 - (6 - 1)x + (6)(-1)
\]
This simplifies to:
\[
x^2 - 5x - 6
\]
Step 4: Identify p and q
From the polynomial \(x^2 + px + q\):
- \(p = -5\)
- \(q = -6\)
Final Values
- \(p = -5\)
- \(q = -6\)
These are the values of \(p\) and \(q\) for the polynomial \(x^2 + px + q\).
To find the roots of the polynomial \(2x^2 - 5x - 3\), we can use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Here, \(a = 2\), \(b = -5\), and \(c = -3\).
Calculating the Discriminant
- \(b^2 - 4ac = (-5)^2 - 4(2)(-3) = 25 + 24 = 49\)
Finding the Roots
\[
x = \frac{5 \pm \sqrt{49}}{4} = \frac{5 \pm 7}{4}
\]
- Roots: \(x_1 = 3\), \(x_2 = -\frac{1}{2}\)
Step 2: Determine the Roots of the First Polynomial
Given that the roots of \(x^2 + px + q\) are double the roots of the second polynomial:
- New roots: \(2x_1 = 6\) and \(2x_2 = -1\)
Step 3: Formulate the Polynomial
The polynomial with roots \(6\) and \(-1\) can be expressed as:
\[
x^2 - (6 - 1)x + (6)(-1)
\]
This simplifies to:
\[
x^2 - 5x - 6
\]
Step 4: Identify p and q
From the polynomial \(x^2 + px + q\):
- \(p = -5\)
- \(q = -6\)
Final Values
- \(p = -5\)
- \(q = -6\)
These are the values of \(p\) and \(q\) for the polynomial \(x^2 + px + q\).
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q?
Question Description
If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q?.
If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q?.
Solutions for If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q? defined & explained in the simplest way possible. Besides giving the explanation of
If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q?, a detailed solution for If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q? has been provided alongside types of If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q? theory, EduRev gives you an
ample number of questions to practice If the zeroes of the polynomial x ^ 2 + px + q are double in value to the zerves of 2x ^ 2 - 5x - 3 find the value of p and q? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup