Question

In Fig. 2.17, the graph of a polynomial p(x) is given. Find the zeros of the polynomial.

Answer 1

Answer:

From the figure, the graph of polynomial p(x) touches the X-axis at 1 point. The graph has 2 same zeroes when it touches at one point.

Hence, the value of of b² - 4ac = 0 and  the number of real zeros of f(x) are : 2 .

**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 ZEROS. 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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