The graph of a polynomial y = f (x), shown in Fig. 2.18. Find the number of real zeros of f (x).
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Answer:
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Answer:
From the figure, the graph of polynomial p(x) intersects X-axis at one point and touches the X-axis at 1 point. The graph has 2 same zeroes when it touches at one point.
Hence, the number of real zeroes are : 3 .
**For any quadratic polynomial ax² + bx + c , the zeros are precisely the x- coordinates of the points where the graph of y = ax² + bx + c intersects the X- axis.
**For any quadratic polynomial the graph of the corresponding equation y = ax² + bx + c has one of the two shapes which are known as parabola either open upwards or open downwards. If a > 0 then the shape of parabola is open upwards or a< 0 then the shape of parabola is open downwards.
•If the graph intersects the X-axis AT TWO POINTS then a quadratic polynomial HAS TWO DISTINCT ZEROES. D= b² - 4ac > 0.
•If the graph intersects or touches the X-axis at EXACTLY ONE POINT then a quadratic polynomial has TWO EQUAL ZEROES (ONE ZERO).D= b² - 4ac = 0.
•If the graph is either completely above X-axis or completely below X-axis axis i.e it DOES NOT INTERSECT X-AXIS axis at any point .Then the quadratic polynomial HAS NO ZERO .D= b² - 4ac < 0.
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