Test: Polynomial Zeros - ACT MCQ

# Test: Polynomial Zeros - ACT MCQ

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## 15 Questions MCQ Test - Test: Polynomial Zeros

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Test: Polynomial Zeros - Question 1

### If the graph of the quadratic polynomial is completely above or below the x-axis, then the nature of roots of the polynomial is _____

Detailed Solution for Test: Polynomial Zeros - Question 1

Since, the graph is completely above or below the x-axis, hence, it has no real roots. If a polynomial has real roots only then it cuts the x-axis. If it lies above or below, the roots are complex in nature.

Test: Polynomial Zeros - Question 2

### Which of the following is not a polynomial?

Detailed Solution for Test: Polynomial Zeros - Question 2

An expression in the form of (x) = a+ a1x + a2x+ … + anxn, where a≠ 0, is called a polynomial where a1, a2 … an are real numbers and each power of x is a non-negative integer.
In case of √x + 2x + 4, the power of x is not an integer.
Therefore it is not a polynomial.

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Test: Polynomial Zeros - Question 3

### Which of the following is a polynomial?

Detailed Solution for Test: Polynomial Zeros - Question 3

An expression in the form of (x) = a+ a1x + a2x+ … + anxn, where a≠ 0, is called a polynomial where a1, a2 … an are real numbers and each power of x is a non-negative integer.
In case of √x + 2x + 4 , the power of √x is not an integer. Similarly for x2/3 + 10x, 2/3 is a fraction.
Now, 5x + 5/x in this case the power of x is a negative integer. Hence it is not a polynomial.

Test: Polynomial Zeros - Question 4

If a < 0, then the graph of ax+ bx + c, has a downward opening.

Detailed Solution for Test: Polynomial Zeros - Question 4

The leading coefficient of the polynomial is less than zero, hence, it has downward opening. For example, the graph of -x2 is

Test: Polynomial Zeros - Question 5

The graph of a quadratic polynomial cuts the x-axis at only one point. Hence, the zeros of the quadratic polynomial are equal and real.

Detailed Solution for Test: Polynomial Zeros - Question 5

If the graph meets x-axis at one point only, then the quadratic polynomial has coincident zeros. Also, the discriminant of the quadratic polynomial is zero, therefore roots will be real.

Test: Polynomial Zeros - Question 6

If the graph of a polynomial cuts the x-axis at 3 points, then the polynomial is ______

Detailed Solution for Test: Polynomial Zeros - Question 6

Since, the graph of the polynomial cuts the x-axis at 3 points, hence, it will be a cubic polynomial. A polynomial is said to be linear, quadratic, cubic or biquadratic according to the degree of the polynomial.

Test: Polynomial Zeros - Question 7

How many points will the graph of x+ 2x + 1 will cut the x-axis?

Detailed Solution for Test: Polynomial Zeros - Question 7

The graph of x+ 2x + 1 does not cut the x-axis, because it has imaginary roots.
x+ 2x + 1 = 0
x+ x + x + 1 = 0
x(x + 1) + (x + 1) = 0
(x + 1)(x + 1) = 0
x = -1, -1

Test: Polynomial Zeros - Question 8

The graph of the polynomial 4x- 8x + 3 cuts the x-axis at ________ and ________ points.

Detailed Solution for Test: Polynomial Zeros - Question 8

The graph of the polynomial cuts the x-axis. Only the zeros of the polynomial cut the x-axis.
4x- 8x + 3 = 0
4x- 6x - 2x + 3 = 0
2x(2x - 3) - 1(2x - 3) = 0
(2x - 3)(2x - 1) = 0

Hence, the graph of the polynomial cuts the x-axis at

Test: Polynomial Zeros - Question 9

If the zeros of a polynomial are 3 and -5, then they cut the x-axis at ____ and _____ points.

Detailed Solution for Test: Polynomial Zeros - Question 9

Since, the zeros of the polynomial are 3 and -5.
Therefore, x = 3 and x = -5 and they cut the x-axis so the y-coordinate will be zero.
Hence, the points it cuts the x-axis will be (3, 0) and (-5, 0).

Test: Polynomial Zeros - Question 10

The biquadratic polynomial from the following is ______

Detailed Solution for Test: Polynomial Zeros - Question 10

A biquadratic polynomial has highest power 4.
Hence, the polynomial with the highest power as 4 is x- 9 or (x+ 3)(x- 3).

Test: Polynomial Zeros - Question 11

A polynomial is said to be linear, quadratic, cubic or biquadratic according to the degree of the polynomial.

Detailed Solution for Test: Polynomial Zeros - Question 11

The degree of the polynomial is the highest of the degree of the polynomial. Hence, a polynomial with highest degree one is linear, two as quadratic and so on.

Test: Polynomial Zeros - Question 12

A real number is called zeros of the polynomial p(x) if _________

Detailed Solution for Test: Polynomial Zeros - Question 12

A number is called zero of polynomial when it satisfies the equation of the polynomial.

Test: Polynomial Zeros - Question 13

What will be the nature of the zeros of a quadratic polynomial if it cuts the x-axis at two different points?

Detailed Solution for Test: Polynomial Zeros - Question 13

The zeros of the quadratic polynomial cut the x-axis at two different points.
∴ b2 – 4ac ≥ 0
Hence, the nature of the zeros will be real and distinct.

Test: Polynomial Zeros - Question 14

The graph of the quadratic polynomial -x+ x + 90 will open upwards.

Detailed Solution for Test: Polynomial Zeros - Question 14

The graph of the polynomial will have a downward opening since, a < 0
The graph for the same can be observed here,

Test: Polynomial Zeros - Question 15

The graph of the polynomial 2x- 8x + 5 cuts the y-axis at __________

Detailed Solution for Test: Polynomial Zeros - Question 15

The graph of the polynomial 2x- 8x + 5 cuts the y-axis.
Hence, the value of x will be 0.
y(0) = 2(0)- 8(0) + 5
y = 5
The graph cuts the y-axis at (0, 5)

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