MCQ : Polynomials - 1


10 Questions MCQ Test Mathematics (Maths) Class 10 | MCQ : Polynomials - 1


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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. The solved questions answers in this MCQ : Polynomials - 1 quiz give you a good mix of easy questions and tough questions. Class 10 students definitely take this MCQ : Polynomials - 1 exercise for a better result in the exam. You can find other MCQ : Polynomials - 1 extra questions, long questions & short questions for Class 10 on EduRev as well by searching above.
QUESTION: 1

If 5 is a zero of the quadratic polynomial, x2 - kx - 15 then the value of k is

Solution:

x=5

putting x in equation

p(x)=x2-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)x2 + kx + 1 is -3, then the value of k is

Solution:

 (k - l)x2 + 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 x2 + ax + b is the negative of the other, then it

Solution:

Let p(x) = x2 + ax + b.
Put a = 0, then,  p(x) = x2 + b = 0
⇒    x= -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) = x2 + ax+ b
and by given condition the zeroes area and – α.
Sum of the zeroes = α- α = a
=>a = 0
f(x) = x2 + b, which cannot be linear,
and product of zeroes = α .(- α) = b
⇒ -α2 = 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 x2 + (a + 1) x + b are 2 and -3, then

Solution:

 x2 + (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) = ax2 + 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 ax2 + bx + c, a≠0, the graph of the Corresponding equation y = ax2 + 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) = 5y2 + 13y + m is reciprocal of other, then the value of m is

Solution:

QUESTION: 10

If p(x) = ax2 + bx + c, then - b/a is equal to 

Solution:

Sum of zeroes = -b/a

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