Mathematics Textbook of Competency Based Questions for Class X>Chapter 2 - Polynomials>Exercise>Q 9

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10th CBSE

IMPORTANT

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Two polynomials are shown in the graph below. Find the number of zeroes that are common to both polynomials. Explain your answer.

Important Questions on Polynomials

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 2 - Polynomials>Exercise>Q 15

If $α$ and $β$ are the zeroes of polynomial $x^{2} + 8 x + 6$ . Form a polynomial whose zeroes are $α - β and α + β$ .

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.