Quadratic EquationsA quadratic equation in x is an equation that can bewritten in the general formax2 + bx + c = 0Where a, b, and c are real numbers, a=0The Quadratic FormulaGiven: ax2+bx+c=0 we can use the quadratic formula x=1. If b2-4ac 0,then there are two distinct real roots2. If b2-4ac 0, then there are two equal real roots 3. If b2-4ac 0, then there are no real roots : Quadratic EquationsA quadratic equation in x is an equation that can bewritten in the general formax2 + bx + c = 0Where a, b, and c are real numbers, a=0The Quadratic FormulaGiven: ax2+bx+c=0 we can use the quadratic formula x=1. If b2-4ac 0,then there are two distinct real roots2. If b2-4ac 0, then there are two equal real roots 3. If b2-4ac 0, then there are no real roots
Slide 2 : Que. Find the nature of the roots of the following quadratic equations. If the real roots exits, find them:
Slide 3 : Que Find the values of k for each of the following quadratic equations, so that they have two equal roots,
Slide 4 : Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.
Slide 5 : Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Slide 6 : Is it possible to design a rectangular park of perimeter 80 m and area 400m2? If so, find its length and breadth.
QUADRATIC EQUATIONS : QUADRATIC EQUATIONS A polynomial of degree 2 is called a quadratic polynomial. Its general form is ax2+bx+c, where a, b, c R such that a ? 0 and x is a variable.
If p(x) = ax2+bx+c is a quadratic polynomial and let a be a real number. Then aa2+ba+c is known as the value of the quadratic polynomial p(x) and it is denoted by p(a).
i.e. P(a)=aa2+ba+c
A real no. a is called a zero of a quadratic polynomial
p(x) = ax2+bx+c, if p(a) =0
If p(x) is a quadratic polynomial, then p(x) = 0 is called a quadratic equation. Its general form is ax2+bx+c = 0,
where a, b, c R and a ? 0