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This mock test of MCQ : Polynomials - 1 for Class 10 helps you for every Class 10 entrance exam.
This contains 10 Multiple Choice Questions for Class 10 MCQ : Polynomials - 1 (mcq) to study with solutions a complete question bank.
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students definitely take this MCQ : Polynomials - 1 exercise for a better result in the exam. You can find other MCQ : Polynomials - 1 extra questions,
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QUESTION: 1

If 5 is a zero of the quadratic polynomial, x^{2} - kx - 15 then the value of k is

Solution:

x=5

putting x in equation

p(x)=x^{2}-kx-15=0

=(5)^{2}-k(5)-15=0

=25-5k-15=0

=10-5k=0

=-5k=-10

=k=-10/-5

=k=2

Value of k is 2

QUESTION: 2

If p(x) is a polynomial of at least degree one and p(k) = 0, then k is known as

Solution:

(b)

Zero of p(x)

Let p(x) = ax + b

Put x = k

p(k) = ak + b = 0

∴ is zero of p(x)

QUESTION: 3

The zero of the polynomial p(x) = 2x + 5 is

Solution:

Given, p(x) = 2x+5

For zero of the polynomial, put p(x) = 0 ∴ 2x + 5 = 0

⇒ -5/2

Hence, zero of the polynomial p(x) is -5/2.

QUESTION: 4

If one of the zeroes of the quadratic polynomial (k - 1)x^{2} + kx + 1 is -3, then the value of k is

Solution:

(k - l)x^{2} + kx +1

One zero is - 3, so it must satisfy the equation and make it zero

QUESTION: 5

If one of the zeros of a quadratic polynomial of the form x^{2} + ax + b is the negative of the other, then it

Solution:

Let p(x) = x^{2} + ax + b.

Put a = 0, then, p(x) = x^{2} + b = 0

⇒ x^{2 }= -b

⇒ x = ± ±**√**-b

[∴b < 0]

Hence, if one of the zeroes of quadratic polynomial p(x) is the negative of the other, then it has no linear term i.e., a = O and the constant term is negative i.e., b< 0.

Alternate Method

Let f(x) = x^{2} + ax+ b

and by given condition the zeroes area and – α.

Sum of the zeroes = α- α = a

=>a = 0

f(x) = x^{2} + b, which cannot be linear,

and product of zeroes = α .(- α) = b

⇒ -α^{2} = b

which is possible when, b < 0.

Hence, it has no linear term and the constant term is negative.

QUESTION: 6

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

Solution:

x^{2} + (a + 1)x + b

∵ x = 2 is a zero and x = - 3 is another zero

QUESTION: 7

The number of polynomials having zeros as - 2 and 5 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: 8

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

Solution:

For any quadratic polynomial ax^{2} + bx + c, a≠0, the graph of the Corresponding equation y = ax^{2} + bx + c has one of the two shapes either open upwards like u or open downwards like ∩ depending on whether a > 0 or a < 0. These curves are called parabolas.

Also, the curve of a quadratic polynomial crosses the X-axis on at most two points but in option (a) the curve crosses the X-axis on the three points, so it does not represent the quadratic polynomial.

QUESTION: 9

If one root of the polynomial p(y) = 5y^{2} + 13y + m is reciprocal of other, then the value of m is

Solution:

QUESTION: 10

If p(x) = ax^{2} + bx + c, then - b/a is equal to

Solution:

Sum of zeroes = -b/a

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