Watch the sixth video session on “Quadratic Equations” for Class Xth – concepts and solved questions.
Quadratic Equations – Class X – Part 6
When we equate quadratic polynomial of the form ax2 + bx + c, to zero, we get a quadratic equation.
A quadratic equation in the variable x is an equation of the form ax2 + bx + c = 0, where a, b, c are real numbers, a ≠ 0. Any equation of the form p(x) = 0, where p(x) is a polynomial of degree 2, is a quadratic equation. ax2 + bx + c = 0, a ≠ 0 is called the standard form of a quadratic equation.
A real number α is called a root of the quadratic equation
ax2 + bx + c = 0, a ≠ 0 if aα2 + bα + c = 0.
A quadratic polynomial can have at most two zeroes. So, any quadratic equation can have atmost two roots.
The roots of ax2 + bx + c = 0 are [-b+√(b2 – 4ac)]/2a and [(-b-√(b2 – 4ac)]/2a, if b2 – 4ac ＞= 0. If b2 – 4ac ＜ 0, the equation will have no real roots.
EXERCISE 4.3 Q7-11 Solved
7. The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
8. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
9. Two water taps together can fill a tank in 9 3/8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
10. An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the two trains.
11. Sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24 m, find the sides of the two squares.