Watch the fifth video session on “Quadratic Equations” for Class Xth – concepts and solved questions.
Quadratic Equations – Class X – Part 5
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 Q3-6 Solved
3. Find the roots of the following equations:
(i) x – (1/x) = 3, x ≠ – 4, 7
(ii) [1/(x+4) – 1/(x-7)] = 11/30 , x ≠ – 4, 7
4. The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age.
5. In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
6. The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.