Polynomials Test

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Polynomials Test - 8

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Weekly Quiz Competition

Question 1
1 / -0

If the graph of a polynomial intersects the x – axis at three points, then the number of zeroes =

A
at least three

B
0

C
3

D
at most three

Solution

If the graph of a polynomial intersects the x-axis at three points, then the number of zeroes are 3 because the x- axis is intersected three times by the three coordinates so,
number of zeroes of the polynomial = number of the coordinates of the points (where its graph intersects the x-axis.)
Question 2
1 / -0

The graph of the polynomial f(x) = 2x – 5 intersects the x – axis at

A
(52 , 0)

B
(−52 , 0)

C
(52 , 52)

D
(52 , −52)

Solution

graph f(x) = 2x - 5 is on x- axis (when the graph is on x-axis then the y point (ordinate) is 0)

put f(x)=0

2x - 5=0

2x = 5

x = 5/2 so the coordinates of graph is (5/2,0)
Question 3
1 / -0

The graph of a cubic polynomial x³ – 4x meets the x – axis at ( – 2, 0), (0, 0) and (2, 0), then the zeroes of the polynomial are

A
0, 0 and 2

B
– 2, 0 and 0

C
– 2, 0 and 2

D
None of these

Solution

n each points (-2,0), (0,0) and (2,0) all in x- axis and each points intersect the graph of cubic polynomials.

so, the number zeroes are -2,0 and 2 (which is coordinates of x-axis)
Question 4
1 / -0

If one zero of the polynomial p( x ) = ( k + 4 )x²+ 13x + 3k is reciprocal of the other, then the value of ‘k’ is

A
4

B
2

C
3

D
5

Solution

Let one zero of the given polynomial be α

the other zero is reciprocal be 1/α.

∵∵ (Products of Roots) αβ=c/a

α × 1 / α = 3k / k+4

1 = 3k / k+4

k + 4 = 3k (by cross multiplication)

4 = 3k-k

4= 2k

k=4/2

k=2
Question 5
1 / -0

The sum of two zeroes of the polynomial f(x)=2x²+(p+3)x+5 is zero, then the value of ‘p’ is

A
3

B
– 3

C
– 4

D
4

Solution

Let zeroes of the given polynomial be α and β.

According to the question, α + β = 0

−b / a = 0
−(p+3) / 2 = 0

⇒ -(p + 3) = 0 (by cross multiplication)

⇒ p = - 3
Question 6
1 / -0

A polynomial whose sum and product of zeroes are – 4 and 3 is

A
x2+4x+3

B
None of these

C
x2−4x+3

D
x²−4x−3

Solution

x²- (Sum the Zeroes )x + (Product of Zeroes)

x² - (-4)x + 3

= x² + 4x + 3

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Polynomials Test - 8

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Polynomials Test - 8

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SHARING IS CARING

Question 1

at least three

0

3

at most three

Solution

Question 2

(52 , 0)

(−52 , 0)

(52 , 52)

(52 , −52)

Solution

Question 3

0, 0 and 2

– 2, 0 and 0

– 2, 0 and 2

None of these

Solution

Question 4

4

2

3

5

Solution

Question 5

3

– 3

– 4

4

Solution

Question 6

x2+4x+3

None of these

x2−4x+3

x2−4x−3

Solution

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x²−4x−3