bovingal a ph respectively, and if p denotes the distance of a point P = (x, y) from the line l, then the locus of all points satisfying pip3 P4 = ap2P5 is given by аpгPs %3D %3D d (a +x)(a - x)(2a – x) = axy. diw bo This locus, which occurs in La Géométrie, was later called the Cartesian parabola, or trident, by Newton. bile 4. Show that the equation xr – x² + 2x +1= 0 has no positive roots. [Hint: Multiply by x + 1, which does not change the number of positive roots.] taird %3D 5. Find the number of positive roots of the equation x’ + 2x³ – x² + x – 1 = 0. %3D 6. From Descartes's rule of signs, conclude that the equation x2" – 1 = 0 has 2n – 2 imaginary roots. 7. Without actually obtaining these roots, show that (a) x³ +3x +7 = 0 and (b) x6 – 5x³ – 7x² + 8x + 20 = 0 %3D %3D both possess imaginary roots. 8. Verify the following assertions. If all the coefficients of an equation are positive and the equation involves no odd powers of r (a) then all its roots are imgi

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.