(i) The number of zeroes is \(0\) as the graph does not cut the x-axis at any point.
(ii) The number of zeroes is \(1\) as the graph intersects the x-axis at only \(1 \) point.
(iii) The number of zeroes is \(3\) as the graph intersects the x-axis at \(3\) points.
(iv) The number of zeroes is \( 2\) as the graph intersects the x-axis at \(2 \) points.
(v) The number of zeroes is \(4 \)as the graph intersects the x-axis at \(4\) points.
(vi) The number of zeroes is \(3 \) as the graph intersects the x-axis at \(3 \) points
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(i) \(x^2 – 2x – 8\) (ii) \(4s^2 – 4s + 1\) (iii) \(6x^2 – 3 – 7x\) (iv) \(4u^2 + 8u\) (v) \( t^2 – 15\) (vi) \(3x^2 – x – 4\)
Graphical representation needs the plotting of the x and y in graph paper. Plotting the x and y values of the equation on the coordinate plane. For plotting the graph you will be needed at least 3 sets of points. It is very much important for those points to fall in a straight line. If the points are haphazardly placed, it will indicate some fault in your work.
On the graph paper, draw the x and y-axis. Simply, the x and y-axis are two number lines that are placed perpendicular to each other at the (0,0) point. This point is known to be the origin. Use the aforesaid values for plotting the points. Join all of these points with a straight line.