quadratic equation for grade 10

1. Quadratic Equation
Chapter 1
Exercise 1.1
Page# 1-5

2. • A quadratic equation is an equation of the second degree, meaning it
contains at least one term that is squared. The standard form is
ax² + bx + c = 0 with a, b, and c being constants, or numerical
coefficients, and x is an unknown variable.
• OR
• An equation which contains the square of the unknown quantity, but
no higher power, is called a quadratic equation or an equation of
second degree
• A second degree equation in one variable x of the form
ax²+ bx+ c=0 is standard or general form of quadratic equation

3. Standard form of quadratic equation
• ax² + bx + c = 0
• 3a+20= -2x²
• 4b²-3b=-10
• 3x²+ 6x+6=0
• 5x²-5x+10=0

4. Solution of Quadratic Equation
• To ways to find solution
1. Factorization
2. Completing square

5. By Factorization
• By Middle term breaking
Write the equation as ax²+ bx+ c=0 e.g.,
x²-x=20
x² - x – 20=0
x² -5x + 4x – 20=0
X(x-5) +4(x-5)=0
(x-5)(x+4)=0
X=+5, -4

6. By Completing Square
• For this method remember the formulae
• (x + y)² = (x²+y²+2xy)
• (x – y)²= (x²+y² - 2xy)
• 7x²+ 2x – 1=0
• 7x²+2x=1
• Dividing both sides by 7
• 7x²/7 +2x/7 = 1/7
• x² + 2x/7 = 1/7

7. • For completing square we have to complete the formula
• x² + 2x/7 = 1/7
• (x)² + 2(x)(1/7) +(1/7)² = 1/7 + (1/7)²
• (x + 1/7)² =1/7 + 1/49
• (x + 1/7)²=1+7/49
• (x + 1/7)²=8/49
• Taking square root on both sides
• (x + 1/7)²=8/49
• √(x + 1/7)²= √8/49
• x + 1/7=2 √2/7
• X=-1/7 +2 √2/7
• X= -1 + 2 √2/7 , -1 -2 √2/7