Watch the third video session on “Quadratic Equations” for Class Xth – concepts and solved questions.
Quadratic Equations – Class X – Part 3
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.
EXERCISE 4.2 Q3-6 Solved
3. Find two numbers whose sum is 27 and product is 182.
4. Find two consecutive positive integers, sum of whose squares is 365.
5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
6. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs. 90, find the number of articles produced and the cost of each article.