Question

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

Answer 1

SOLUTION :  

From the figure, the graph of polynomial p(x) intersects X-axis at two points.(-3,0) & (-1,0)

Hence,  the zeroes of p(x) are : -3 & -1

**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 ZEROES.D= b² - 4ac > 0.

•If the graph intersects 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…

Answer 2

Hola User ____________________⭐

Here is Your Answer....!!!
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〽↖Actually welcome to the concept of the Quadratic Equations ...

〽↖Basically the graph of the Quadratic Equations is a Parabola always ...

〽↖So now here to get the solution or roots of the polynomial p (x) .....
the roots are those where the Value of X is such that ...after substituting it gives us value as Zero ....

〽↖So the values of the x that can give us zero are

〽⤵X = -3 and X = -1 ....this is where the graph cuts The x-axis and thus they are the roots of the equation ....

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⭐Hope it helps u.....☺