Draw the graphs of the givenpolynomials and answer the following questions:1.2x + 3 a)Name the type of polynomial1.b)What is the graph of thepolynomial?c)At how many points does the graphcut the x axis?d)Maximum at how many points the graph of a polynomial of degree 1can cut the x axis?e)How many zeroes does the polynomial1 have?f)What is the zero of the polynomial1?2.x23.x2–3x –4 4.-2x2+ 1a)Nametypeof polynomials represented by2 , 3and 4.b)Namethe graph of these polynomials?c)At howmany places does the graph of polynomial2 cut the x axis?d)At how many places does the graph of polynomial3 cut the x axis?e)Is it necessary for a graph of a polynomial of degree 2 to cut the x axis at 2 points?f)Maximum at how many points the graphof the polynomial of degree 2can cut the x axis?g)What are the zeroes of the polynomial2?h)What are thezeroes of thepolynomial3?i)What are the zeroes of the polynomial4?j)Is the graph of the polynomial4open upwards or down wards? Why?5.x3–2xa)Write the type ofpolynomial5.b)At how many places does thegraph cut the x axis?c)How many zeroes does the polynomial5 have?d)What are the zeroes of the polynomial 5?
Answers
(1) 2x + 3
a) Name the type of polynomial ?
b) What is the graph of the polynomial ?
c) At how many points does the graph cut the x axis ?
d) Maximum at how many points the graph of a polynomial of degree 1 can cut the x axis ?
e)How many zeroes does the polynomial 1 have ?
f) What is the zero of the polynomial 1 ?
Answer :-
2x + 3 :-
a) Linear polynomial .
b) Graph of a linear polynomial is a straight line .
c) The graph cut the x axis at 1 point .
d) The graph of a polynomial of degree 1 can cut the x axis at maximum 1 point .
e) Polynomial 1 have 1 zero .
f) 2x + 3 = 0 => x = (-3/2) = (-1.5) .
(2) x²–3x –4
a) Name type of polynomials represented by .
b) Name the graph of these polynomials ?
c)At how many places does the graph of polynomial 2 cut the x axis ?
d) What are the zeroes of the polynomial 2 ?
Answer :-
x² - 3x - 4 :-
a) Quadratic polynomial .
b) The graph of a quadratic function is a U shaped curve called a parabola .
c) The graph of polynomial 2 cut the x axis at 2 points .
d) x² - 3x - 4 = 0 => x² - 4x + x - 4 = 0 => x(x - 4) + 1(x - 4) = 0 => (x - 4)(x + 1) = 0 => x = 4 and (-1) .
(3) x³–2x
a) Write the type of polynomial ?
b) At how many places does the graph cut the x axis ?
c) How many zeroes does the polynomial have ?
Answer :-
a) Cubic polynomial .
b) The graph of polynomial cut the x axis at 3 points .
c) The polynomial have 3 zeroes .
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