Mathematics Textbook of Competency Based Questions for Class X>Chapter 2 - Polynomials>Exercise>Q 35

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10th CBSE

IMPORTANT

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A graph of a cubic polynomial is plotted on a graph paper.

What is the sum of the roots of the polynomial?

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Important Questions on Polynomials

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 2 - Polynomials>Exercise>Q 16

If

α

and

β

are the zeros of the quadratic polynomial

f (x) = x^{2} - 3 x - 2

, find a quadratic polynomial whose zeros are

\frac{1}{2 α + β}

and

\frac{1}{2 β + α}

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 2 - Polynomials>Exercise>Q 17

If the zeroes of the cubic polynomial

x^{3} - 6 x^{2} + 3 x + 10

are of the form

a, a + b

and

a + 2 b

for some real numbers

a

and

b

, find the values of

a

and

b

as well as the zeroes of the given polynomial.

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 2 - Polynomials>Exercise>Q 18

If

a (70 a - 12 b + 2 c) > 0

and the quadratic equation

a x^{2} + b x + c = 0

real roots

α

and

β

, then which of the following statements is always false?

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 2 - Polynomials>Exercise>Q 21

Draw the graph of

y = x^{2} - 4

and hence solve

x^{2} - x - 12 = 0

.

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 2 - Polynomials>Exercise>Q 30

If

α

and

β

are zeroes of the quadratic polynomial

k x^{2} + 4 x + 4

such that

α^{2} + β^{2} = 24

, then find the value of

k ?

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 2 - Polynomials>Exercise>Q 31

Find the value of

k,

such that one zero of the polynomial

3 x^{2} + (1 + 4 k) x + k^{2} + 5

is one third of other.