Quadratic Equations | Practice Set 2.1 | Mahesh Prajapati

Here you will learn Practice set 2.1 of 10th Maths 1 Quadratic Equations by Mahesh Prajapati.

You have studied polynomials last year. You know types of polynomials according to their degree. When the degree of polynomial is 1 it is called a linear polynomial and if degree of a polynomial is 2 it is called a quadratic polynomial.

Standard form of quadratic equation

The equation involving one variable and having 2 as the maximum index of the variable is called the quadratic equation.
General form is ax2 + bx + c = 0
In ax2 + bx + c = 0, a, b, c are real numbers and a is not equal to 0.
ax2 + bx + c = 0 is the general form of quadratic equation.

Click here for Practice Set 1.1 Elimination Method

Roots of a quadratic equation

In the previous class you have studied that if value of the polynomial is zero for x = a then (x – a) is a factor of that polynomial. That is if p(x) is a polynomial and p(a) = 0 then (x – a) is a factor of p(x). In this case ’a’ is the root or solution of p(x) = 0

Practice Set 2.1

  1. Write any two quadratic equations.
  2. Decide which of the following are quadratic equations.
    (1) x2 + 5 x – 2 = 0 (2) y2 = 5 y – 10 (3) y2 + 1/y = 2
    (4) x +1/ x = -2 (5) (m + 2) (m – 5) = 0 (6) m3 + 3 m2 -2 = 3 m3
  3. Write the following equations in the form ax2 + bx + c = 0, then write the values of a, b, c for each equation.
    (1) 2y =10 – y2 (2) (x – 1)2 = 2 x + 3 (3) x2 + 5x = -(3 – x)
    (4) 3m2 = 2 m2 – 9 (5) P (3 + 6p) = -5 (6) x2 – 9 = 13
  4. Determine whether the values given against each of the quadratic equation are the
    roots of the equation.
    (1) x2 + 4x – 5 = 0 , x = 1, -1 (2) 2m2 – 5m = 0 , m = 2, 5/2
  5. Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0 .

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