Question

The graph of the polynomial f(x) = ax² + bx + c is as shown below (Fig. 2.19). Write the signs of 'a' and b² – 4ac.

Answer 1

Given : The graph of the polynomial f(x) = ax² + bx + c  

Figure is in the attachment below .

 

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

 

Concept :  

• **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…

 

Some more questions :  

The graph of the polynomial $f(x)= ax^{2}+bx+c$ is as shown in Fig. 2.20. Write the value of $b^{2}-4ac$ and the number of real zeros of f(x).

https://brainly.in/question/5911437

The graph of a polynomial f(x) is as shown in Fig. 2.21. Write the number of real zeros of f(x).

https://brainly.in/question/5911465

Answer 2

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…