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This mock test of Test: Polynomials (Medium) for Class 10 helps you for every Class 10 entrance exam.
This contains 20 Multiple Choice Questions for Class 10 Test: Polynomials (Medium) (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Find the zeros of a quadratic polynomial √3x^{2} - 8x + 4√3.

Solution:
Given quadratic equation = √3x² - 8x + 4√3 = 0

We should factorize the equation first. =√3x² - 6x - 2x + 4√3 = 0

= √3x(x - 2√3) - 2(x - 2√3) = 0

= (√3x - 2) (x - 2√3) = 0

= (√3x - 2) = 0, (x - 2√3) = 0

= x = 2 / √3 , x = 2√3.

QUESTION: 2

Write the degree of the given polynomial: 2p - √7.

Solution:
The highest power of the variable in a polynomial in one variable is called the **degree** of the polynomial.

QUESTION: 3

Find the degree of the polynomial 5t + √7.

Solution:
The degree is the highest power of the variable in the polynomial.

QUESTION: 4

Find the smallest solution in positive integers of x^{2} - 14y^{2} = 1.

Solution:
x^{2} − 1 = 14y^{2}

Now checking by putting y = 1, 2, 3... until we get solution

y = 1; => x^{2} =15 not possible

y = 2; => x^{2} = 57 not possible

y = 3; => x^{2} = 127 not possible

y = 4; => x^{2} = 225 => x = 15

Hence, the smallest solution is (x, y) = (15, 4).

QUESTION: 5

Find the zeroes of the quadratic polynomial from the graph.

Solution:
Given polynomial graph cuts the x-axis at 2 points. So, it must have two roots. Here the x-coordinates of (-2, 0) and (3, 0) are the two zeroes of the quadratic polynomial.

QUESTION: 6

If one zero of polynomial (k^{2} + 16) x^{2} + 16x + 8k is reciprocal of the other, them k is equal to

Solution:

QUESTION: 7

The graph of f(x) is shown below. The number of zeroes of f(x) are:

Solution:

QUESTION: 8

The graph of a quadratic polynomial p(x) = ax^{2} + bx + c is a parabola, opening downwards if

Solution:

QUESTION: 9

Sum of the zeroes of the polynomial p(x) = - 3x^{2} + a is

Solution:

QUESTION: 10

The sum and product of zeroes of a quadratic polynomial are - 1 and - 6 respectively. The quadratic polynomial is given by

Solution:
Quadratic equation given sum and product of zeros is,

p(x) = x² - x (sum of zeros) + product of zeros

p(x) = x² - x (-1) + (-6)

p(x) = x² + x - 6

QUESTION: 11

Number of zeroes of a polynomial of degree n is

Solution:
A polynomial of n degree can have n zeros. For example, a quadratic equation ax^{2} + bx + c = 0 can have 2 zeros, as the highest power of x is 2 or as the degree is 2. ax^{3} + bx^{2} + cx + d = 0, a cubic equation can have 3 zeros, as the highest power of x is 3 or as the degree is 3.

QUESTION: 12

Number of quadratic polynomials having - 2 and - 5 as their two zeroes is

Solution:
Let p (x) = ax^{2} + bx + c be the required polynomial whose zeroes are -2 and 5.

Hence, the required number of polynomials are infinite i.e., more than 3.

QUESTION: 13

Which of the following is not a graph of a quadratic polynomial?

Solution:

QUESTION: 14

If one zero of the quadratic polynomial 39 y^{2} - (2k + 1)y - 22 is negative of the other, then the value of k is

Solution:

QUESTION: 15

If α and β are zeros of a quadratic polynomial such that α + β = 12 and α - β = 6. Them, the family of quadratic polynomials having α, β as its zeroes is given by

Solution:

QUESTION: 16

If α, β, γ are the zeroes of the polynomial p(x) = x^{3} + 6x^{2} + cx + d, such that α + β = 2, then the value of γ is

Solution:
Sum of roots = −b / a = −6

⇒ α + β + γ = −6

⇒ 2 + γ = −6

⇒ γ = −8

QUESTION: 17

If the zeroes of the quadratic polynomial x^{2} + (a +1) x + b are 2 and - 3, then

Solution:
Thus, 2 + (−3) = 1 − (a + 1)

=> 1 (a + 1) = 1

=> a + 1 = 1

=> a = 0

Also, 2 × (−3) = b = -6

QUESTION: 18

When x^{4} + x^{3} - 2x^{2} + x + 1 is divided by x - 1, them the remainder is

Solution:

QUESTION: 19

If α and β are the zeroes of the quadratic polynomial p(x) = x^{2} + 2x - k such that α^{2} + β^{2} = 34, then the value of k is

Solution:
α + β = -b / a

α + β = -2

α x β = c / a

α x β = -k

Now, α^{2} + β^{2} = 34

using identity we get

(α + β)^{2} - 2α x β

Now putting up the values

(-2)^{2} - 2 x -k = 34

4 + 2k = 34

2k = 30

k = 15.

QUESTION: 20

If the sum of products of zeroes taken, two at a time of polynomial p(x) = x^{3} - 5x^{2} + kx + 8 is 2, then the value of k is

Solution:

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