Slide 1 : QUDRATIC EQUATIONS
Slide 2 : 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. For example, 2x2 + x – 300 = 0 is a quadratic equation.
Similarly, 2x2 – 3x + 1 = 0, 4x – 3x2 + 2 = 0 and 1 – x2 + 300 = 0 are also quadratic equations.
The general form of the quadratic equation is ax2 +bx +c =o : The general form of the quadratic equation is ax2 +bx +c =o Factorize the following:
x2 - 10x - 11 = 0 2) x2 + 4x - 21 = 0
Slide 4 : 3) x2 - 14x + 45 = 0
Slide 5 : The formula for finding the roots of a quadratic equation is known as the quadratic formula. The quadratic formula is
Slide 6 : Solve the following using quadratic formula
x2-5x+4=0
2) x2-7x-18=0
Slide 7 : 3)5x2-x-4=0
4)3x2+2x-8=0
Slide 8 : Nature of the roots :
In x=- b ±?b2 – 4ac
b2 –4ac is known as discriminant
If b2 – 4ac=o Roots are real and equal
if b2– 4ac = 0 Roots are real and unequal
if b2 –4ac = 0 Roots are are imaginary or no roots 2a
Slide 9 : Examine the nature of the roots
3x2 + 2x—1 =0
6x2—5x—6 =0
3) x2—6x—9 =0
Slide 10 : Find the value of k for which the roots are
real and equal
1)kx2+4x+1=o
2)3x2—5x+2k =0
Slide 11 : Find the value of k for which the roots are
real and distinct
1)2x2+3x+ k =0
2)kx2+6x +1 =0
Slide 12 : 3) x2—kx +9 =0
4)2x2 +kx – 4 =0
5)4x2—3kx +1 =0
Sum and product of the roots : Sum and product of the roots ax2 + bx +c=0
Slide 14 : Find the sum and product of roots
4x2+2x—1 =0
8x2– 3x +4 =0
3. 9x2+30x+25=0
Slide 15 : Find the quadratic equation whose roots have the sum and product as
sum =3 and product =2
2) sum =8 and product = -- 9 Formation of quadratic using sum and product of roots
Slide 16 : 3.sum =2?5 and product =5
4.sum =--5?2 and product =-- 28
Slide 17 : Find the quadratic equation whose root are
8 and 3
9 and – 3
7 and –5
Slide 18 : 4).?2 and 2?2
5.)?3 and 5?3
Slide 19 : 6.) 1+?2 and 1-- ?2
7)4 -- ?5 and 4+?5
8)7+?7 and 7-- ?7