Question

14) The graph of the polynomial f(x) = ax? + bx + c is as shown below (Fig. 2.19). Write the
signs of 'a' and b2 - 4ac and c.
у
AY
y = f(x)
X'
o
​

Answer 1

Answer:

Step-by-step explanation:

SOLUTION :

From the figure, the graph of polynomial p(x) intersects X-axis axis at two points.

Hence, the sign of ‘a’ is > 0 and b² - 4ac > 0

**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.

HOPE THIS ANSWER WILL HELP YOU…