Question

the graph of the polynomial y=ax2+bx+c is shown in the figure.write one value of b2-4ac.

Answer 1

in this quadratic equation x-axis will touch only once 
if the roots of the quadratic equation are equal then the graph toughes x-axis 2 times
we know if roots r equal as well as real the value will be zero
⇒ b²-4ac=0
∴the one value for b²-4ac is  b²-4ac=0

Answer 2

Answer:

The roots of the given polynomial are real and distinct.  

Step-by-step explanation:

Given a graph of the polynomial $y=ax^{2} +bx+c$.

Assuming the curve of the polynomial is as shown in the figure.

• The plotted polynomial is like a parabola with y values increasing in the positive direction.
• The parabola intersects the x-axis at two points, which are the roots of the given polynomial.
• Since the value of y is increasing in the positive direction, therefore the value of $a$ is positive and greater than zero.
• The roots of the polynomial can be given by the quadratic formula

                                            $x=\frac{-b\pm\sqrt{b^{2}-4ac} }{2a}$

• where $\sqrt{b^{2}-4ac}$ is the discriminant and defines the nature of roots of the equation.
• Since, $a > 0$, therefore $b^{2}-4ac > 0$. Hence, the roots are real and distinct.