) Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.
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Option 1
32) (a) The shape of the path traced shown is *
a) Spiral
b) Ellipse
c) Linear
d) Parabola
32)(b) The graph of parabola opens upwards, if _______ *
a) a = 0
b) a < 0
c) a > 0
d) a ≥ 0
32)(c) Observe the following graph and answer.In the given graph, how many zeroes are there for the polynomial? *
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a) 0
b) 1
c) 2
d) 3
32)(d) The three zeroes in the above shown graph are *
a) 2, 3,-1
b) -2, 3, 1
c) -3, -1, 2
d) -2, -3, -1
32)(e) What will be the expression of the polynomial? *
a) x³ + 2x² – 5x – 6
b) x³ + 2x² – 5x + 6
c) x³ + 2x² + 5x – 6
d) x³ + 2x² + 5x + 6
Answers
32) (a) The shape of the path traced shown is :-
a) Spiral
b) Ellipse
c) Linear
d) Parabola
Answer :- d) Parabola .
32) (b) The graph of parabola opens upwards, if _______ *
a) a = 0
b) a < 0
c) a > 0
d) a ≥ 0
Answer :-
- c) a > 0 .
- if asked downward it will be a < 0 .
32) (c) Observe the following graph and answer. In the given graph, how many zeroes are there for the polynomial ?
a) 0
b) 1
c) 2
d) 3
Answer :- d) 3
As we can see that, the graph is cutting x - axis 3 times . so, we can conclude that, there are 3 zeroes for the polynomial .
32) (d) The three zeroes in the above shown graph are :-
a) 2, 3,-1
b) -2, 3, 1
c) -3, -1, 2
d) -2, -3, -1
Answer :-
- The graph is cutting at :- (-3), (-1), and 2 . (c)
32) (e) What will be the expression of the polynomial ?
a) x³ + 2x² – 5x – 6
b) x³ + 2x² – 5x + 6
c) x³ + 2x² + 5x – 6
d) x³ + 2x² + 5x + 6
Answer :-
we have, three roots as ,
- a = (-3)
- b = (-1)
- c = 2
so,
→ Required polynomial = x³ - (a + b + c)x² + (ab + bc + ca)x - abc = 0
putting values we get,
→ Required polynomial = x³ - (-3 - 1 + 2)x² + (-3*-1 - 1*2 - 3*2)x - (-3)*(-1)*2
→ Required polynomial = x³ + 2x² - 5x - 6 (a) .
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