Class 10 Exam  >  Class 10 Questions  >  If the zeroes of the quadratic polynomial (ax... Start Learning for Free
If the zeroes of the quadratic polynomial (ax^2+ bx +c) are both negative ,then, a,b, and c all have same sign. True or false .justify?
Most Upvoted Answer
If the zeroes of the quadratic polynomial (ax^2+ bx +c) are both negat...
Yes. In such cases a, b, c will have same sign.

*Justification*

Both zeros are negative, means, product of zeros positive. So, c/a is positive .

Thus, a and c must be either both positive or negative

Both zeros are negative, means, sum of zeros also negative. So, -b/a is negative ; so , b/a is positive .


Thus, a and b must be either both positive or negative

Therefore, a, b, c will have same sign, either both positive or negative
Community Answer
If the zeroes of the quadratic polynomial (ax^2+ bx +c) are both negat...
Solution:

The given statement is true.

Justification:

Let the zeroes of the quadratic polynomial (ax^2 bx c) be -p and -q. Then we have:

(ax^2 bx c) = a(x+p)(x+q)

Since -p and -q are the zeroes of ax^2 bx c, we have:

a(-p+q)(-p+q+b/a) = 0

Thus, we have the following cases:

Case 1: a > 0

In this case, (-p+q) and (-p+q+b/a) have the same sign. Since -p and -q are both negative, we have:

-p < 0="" and="" -q="" />< />

Adding these inequalities, we get:

-p-q < />

Multiplying both sides by (-p+q+b/a), we get:

(-p+q)(-p+q+b/a) > 0

This implies that (-p+q) and (-p+q+b/a) have the same sign, which means that b/a > 0. Therefore, a, b, and c all have the same sign.

Case 2: a < />

In this case, (-p+q) and (-p+q+b/a) have opposite signs. Since -p and -q are both negative, we have:

-p < 0="" and="" -q="" />< />

Adding these inequalities, we get:

-p-q < />

Multiplying both sides by (-p+q+b/a), we get:

(-p+q)(-p+q+b/a) < />

This implies that (-p+q) and (-p+q+b/a) have opposite signs, which means that b/a < 0.="" therefore,="" a,="" b,="" and="" c="" all="" have="" the="" same="" />

Hence, we can conclude that if the zeroes of the quadratic polynomial (ax^2 bx c) are both negative, then a, b, and c all have the same sign.
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

Top Courses for Class 10

If the zeroes of the quadratic polynomial (ax^2+ bx +c) are both negative ,then, a,b, and c all have same sign. True or false .justify?
Question Description
If the zeroes of the quadratic polynomial (ax^2+ bx +c) are both negative ,then, a,b, and c all have same sign. True or false .justify? 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 quadratic polynomial (ax^2+ bx +c) are both negative ,then, a,b, and c all have same sign. True or false .justify? 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 quadratic polynomial (ax^2+ bx +c) are both negative ,then, a,b, and c all have same sign. True or false .justify?.
Solutions for If the zeroes of the quadratic polynomial (ax^2+ bx +c) are both negative ,then, a,b, and c all have same sign. True or false .justify? 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 quadratic polynomial (ax^2+ bx +c) are both negative ,then, a,b, and c all have same sign. True or false .justify? defined & explained in the simplest way possible. Besides giving the explanation of If the zeroes of the quadratic polynomial (ax^2+ bx +c) are both negative ,then, a,b, and c all have same sign. True or false .justify?, a detailed solution for If the zeroes of the quadratic polynomial (ax^2+ bx +c) are both negative ,then, a,b, and c all have same sign. True or false .justify? has been provided alongside types of If the zeroes of the quadratic polynomial (ax^2+ bx +c) are both negative ,then, a,b, and c all have same sign. True or false .justify? theory, EduRev gives you an ample number of questions to practice If the zeroes of the quadratic polynomial (ax^2+ bx +c) are both negative ,then, a,b, and c all have same sign. True or false .justify? tests, examples and also practice Class 10 tests.
Explore Courses for Class 10 exam

Top Courses for Class 10

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev