NCERT Solution
Class 10
Mathematics
Polynomials
verify that the numbers given alongside of the cub...

Question:
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:

Answer:

(i) Here f(x) = 2x³ + x² - 5x + 2

Given roots of f(x) are ½, 1, -2

F(1/2) = 2×(1/2)³ + (1/2)² - 5(1/2 ) + 2 = 0

F(1) = 2(1)³ + 1² - 5(1) + 2 = 0

F(-2) = 2(-2)³ + (-2)² - 5(-2) + 2 = 0

Hence, ½, 1 and -2 are the zeroes of f(x).

Therefore, sum of zeroes = -b/a -1/2

Sum of product of zeroes taken two at a time = c/a = -5/2

Product of zeroes = -d/a = 2

(ii) Let the f(x) = ax³ + bx² + c + d

Let α, β and γ be the zeroes of the polynomial f(x).

Then, sum of zeroes = -b/a = 2/1 ………………(i)

Sum of product of zeroes taken two at a time = c/a = -7. ………………..(ii)

Product of zeroes = -d/a = -14 ……………….(iii)

From equation (i), (ii) and (iii) we have

a = 1 , b = -2 , c = -7 and d = 14

Therefore the required polynomial on putting the values of a, b, c and d

F(x) = x³ - 2x² - 7x + 14

1
0
0
Report?

Report a problem on Specifications:

Email id:

Comments

Next Question >

SELECT ex_no,question,question_no,id,chapter FROM question_mgmt as q WHERE courseId='9' AND subId='6' AND ex_no!=0 AND status=1 and id!=9507 ORDER BY views desc, last_viewed_on desc limit 0,10

Popular questions of class 10 Mathematics

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.

Is the following situation possible? If so, determine their present ages.
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) x² – 2x – 8 (ii) 4s² – 4s + 1 (iii) 6x² – 3 – 7x (iv) 4u² + 8u (v) t²– 15 (vi) 3x²– x – 4

Find two consecutive positive integers, sum of whose squares is 365.

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

Refer to Example 13. (i) Complete the following table:

(ii) A student argues that ‘there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability

Do you agree with this argument? Justify your answer.

Find two numbers whose sum is 27 and product is 182.

The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:

(i) 2x²– 3x + 5 = 0 (iii) 2x²– 6x + 3 = 0

Prove that 3 + 2√5 is irrational.

SELECT ex_no,question,question_no,id,chapter FROM question_mgmt as q WHERE courseId='9' AND subId='6' AND ex_no!=0 AND status=1 and id!=9507 ORDER BY last_viewed_on desc limit 0,10

Recently Viewed Questions of Class 10 Mathematics

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

Find two consecutive positive integers, sum of whose squares is 365.

Is the following situation possible? If so, determine their present ages.
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Which of the following arguments are correct and which are not correct? Give reasons for your answer.
(i) If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3.

(ii) If a die is thrown, there are two possible outcomes—an odd number or an even number. Therefore, the probability of getting an odd number is 1/2.

Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see Fig. 15.4). What is the probability that the fish taken out is a male fish?

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) x² – 2x – 8 (ii) 4s² – 4s + 1 (iii) 6x² – 3 – 7x (iv) 4u² + 8u (v) t²– 15 (vi) 3x²– x – 4

Question:
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:

< Previous Question

Next Question >

Popular questions of class 10 Mathematics

Recently Viewed Questions of Class 10 Mathematics

Comments

Comment(s) on this Question

NCERT Solutions

Quick Links

Resources

Support

Question: Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:

< Previous Question

Next Question >

Popular questions of class 10 Mathematics

Recently Viewed Questions of Class 10 Mathematics

Comments

Comment(s) on this Question

NCERT Solutions

Quick Links

Resources

Support

Question:
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case: