Math Olympiad Test: Polynomials - 1 - Class 10 MCQ

# Math Olympiad Test: Polynomials - 1 - Class 10 MCQ

Test Description

## 10 Questions MCQ Test Olympiad Preparation for Class 10 - Math Olympiad Test: Polynomials - 1

Math Olympiad Test: Polynomials - 1 for Class 10 2024 is part of Olympiad Preparation for Class 10 preparation. The Math Olympiad Test: Polynomials - 1 questions and answers have been prepared according to the Class 10 exam syllabus.The Math Olympiad Test: Polynomials - 1 MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Math Olympiad Test: Polynomials - 1 below.
Solutions of Math Olympiad Test: Polynomials - 1 questions in English are available as part of our Olympiad Preparation for Class 10 for Class 10 & Math Olympiad Test: Polynomials - 1 solutions in Hindi for Olympiad Preparation for Class 10 course. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free. Attempt Math Olympiad Test: Polynomials - 1 | 10 questions in 10 minutes | Mock test for Class 10 preparation | Free important questions MCQ to study Olympiad Preparation for Class 10 for Class 10 Exam | Download free PDF with solutions
 1 Crore+ students have signed up on EduRev. Have you?
Math Olympiad Test: Polynomials - 1 - Question 1

### If a  and b are the zeros of ax2 + bx + c, find  the value of

Detailed Solution for Math Olympiad Test: Polynomials - 1 - Question 1

Given a and b are the zeros of ax2 + bx+ c
∴

Math Olympiad Test: Polynomials - 1 - Question 2

### If the sum of squares of zeros of the quadratic polynomial P(x) = x2 - 8x + k is 40. What is the value of k?

Detailed Solution for Math Olympiad Test: Polynomials - 1 - Question 2

P(x) = x2 - 8x + k
If α, and β are its zeros
then α + β = 8, αβ = k
and α2 + β2 = 40
⇒ (α + β)2 - 2αβ = 82 - 2k
⇒ 40 = 64 - 2k
⇒ 2k = 24
⇒ k = 12

Math Olympiad Test: Polynomials - 1 - Question 3

### What must be subtracted from 8x4 + 14x3 - 2x2 + 7x - 8 so that the resulting polynomial is exactly divisible by 4x2 + 3x - 2?

Detailed Solution for Math Olympiad Test: Polynomials - 1 - Question 3

Here, (4x2 + 3x - 2) 8x4 + 14x3 - 2x2 + 7x - 8 (2x2 + 2x - 1)

∴ 14x - 10 must be subtracted.

Math Olympiad Test: Polynomials - 1 - Question 4

What is the cubic polynomial in which the sum, sum of the products of its zeros taken at a time and product of its zeros as 2, -7, -14 respectively?

Detailed Solution for Math Olympiad Test: Polynomials - 1 - Question 4

Given a + b+ γ = 2 = ⇒ b = -2a
αβ + βγ + γα = -7 = ⇒ c = -7a
αβγ = -14 = ⇒ d = 14a

b : c : d = -2 : -7 : 14
Cubic polynomial is
k(x3 - 2x2 - 7x + 14)

Math Olympiad Test: Polynomials - 1 - Question 5

If the product of two zeros of the polynomial 2 x3 + 6x− 4x + 9 is 3 then what is its third zero?

Detailed Solution for Math Olympiad Test: Polynomials - 1 - Question 5

If α and β are two zeros then αβ = 3 Let third root be γ.

Math Olympiad Test: Polynomials - 1 - Question 6

If α, β, γ are the zeros of the polynomial 2 x3 + x− 13x + 6. What is the value of αβγ?

Detailed Solution for Math Olympiad Test: Polynomials - 1 - Question 6

The given polynomial is
2 x3 + x− 13x + 6
α,β,γ be its zeros
∴

Math Olympiad Test: Polynomials - 1 - Question 7

What must be added to f(x) = 4x4 + 2x− 2x2 + x − 1 so that the resulting polynomial is divisible by g (x) = x2 + 2x − 3?

Detailed Solution for Math Olympiad Test: Polynomials - 1 - Question 7

Here
(x2 + 2 x — 3)4 x4 + 2 x3 — 2 x2 + x — l(4 x2 — 6 x + 22

Clearly -61x + 65 must be added.

Math Olympiad Test: Polynomials - 1 - Question 8

What is the cubic polynomial whose zeros are α, β, γ such that α + β + γ = 4. αβγ = - 6 and αβ + βγ + γα = 1?

Detailed Solution for Math Olympiad Test: Polynomials - 1 - Question 8

Required polynomial
= P(x ) = x3 - (α + β + γ)x2 + (αβ + βγ + γα)x
- αβγ
Thus, the cubic polynomial is
p(x) = x3 − (4)x2 + (1)x − (−6)
= x3 − 4x2+ x + 6

Math Olympiad Test: Polynomials - 1 - Question 9

Which quadratic polynomial has sum of whose zeros is -5 and product of its zero is -12?

Detailed Solution for Math Olympiad Test: Polynomials - 1 - Question 9

Given data
Sum of zeroes = −5
Product of zeroes = 6
x2 − (sum of zeroes) x + product of zeroes = 0
x2 − (−5)x + 6 = 0
x2 + 5x + 6 = 0

Math Olympiad Test: Polynomials - 1 - Question 10

What are the zeros of x2 - 2x - 3?

Detailed Solution for Math Olympiad Test: Polynomials - 1 - Question 10

We have x2 - 2x - 3
∴

## Olympiad Preparation for Class 10

11 videos|36 docs|201 tests
In this test you can find the Exam questions for Math Olympiad Test: Polynomials - 1 solved & explained in the simplest way possible. Besides giving Questions and answers for Math Olympiad Test: Polynomials - 1, EduRev gives you an ample number of Online tests for practice

## Olympiad Preparation for Class 10

11 videos|36 docs|201 tests