Solving a quadratic equation, Mathematics

Assignment Help:

In polynomials you have seen expressions of the form x2 + 3x - 4. Also we know that when an expression is equated to zero or some other expression, we call it an equation. The equations of the second degree in a single variable "x" or "y" are generally referred to as quadratic equations and the most general form of it is

ax2 + bx + c = 0. The roots or solution for the quadratic equation can be obtained by substituting different values for x and selecting that value for which the value of the equation is zero. The methods which we have seen in factorization of polynomials are also applicable to obtain the roots of a quadratic equation. However, in this part we look at a specific method which is only applicable to solve quadratic equations.

According to this method the roots of a quadratic equation ax2 + bx + c = 0 are

= 2436_quadratic equation1.png and x = 1422_quadratic equation.png

This is derived as follows. We have

         ax2 + bx + c       = 0

         ax2 + bx             = - c                                         ........(1)

On dividing equation (1) by a, we have x2 1418_quadratic equation2.png

In order to make the LHS a perfect square, we add to   2073_quadratic equation3.png  to the LHS and since the equality is to be preserved we do so for the other side also. Hence we obtain

x2 +

2304_quadratic equation4.png



 

2076_quadratic equation5.png 


Related Discussions:- Solving a quadratic equation

Fractions, what Is the common denominator for 1/2 and 1/4

what Is the common denominator for 1/2 and 1/4

Standard errors of the mean, Standard errors of the mean The series of ...

Standard errors of the mean The series of sample means x¯ 1 , x¯ 2 , x¯ 3 ........ is normally distributed or nearly so as according to the central limit theorem. This can be

Find the common difference & write the next 3 terms, If the following terms...

If the following terms form a AP. Find the common difference & write the next 3 terms3, 3+ √2, 3+2√2, 3+3√2.......... Ans:    d= √2 next three terms 3 + 4 √ 2 , 3 + 5√ 2 ,

Geometry, if two circles O and O''intersect in two points, A and B, the the...

if two circles O and O''intersect in two points, A and B, the the line segment OO is what?

Group automorphism, (a) Find an example of groups G, H, K with K  H and H...

(a) Find an example of groups G, H, K with K  H and H G but K G. (b) A subgroup H of G is characteristic if σ(H) ⊆ H for every group automorphism σ of G. Show that eve

Probability, TWO PERSONS A AND B AGREE TO MEET AT A PLACE BTWEEN 11 TO 12 N...

TWO PERSONS A AND B AGREE TO MEET AT A PLACE BTWEEN 11 TO 12 NOON.  THE FIRST ONE TOARRIVE WAITS FOR 20 MIN AND THEN LEAVE. IF THE TIME OF THIR ARRIVAL BE INDEPENDET AND AT RNDOM,T

Center of mass - applications of integrals, Center of Mass - Applications o...

Center of Mass - Applications of integrals In this part we are going to find out the center of mass or centroid of a thin plate along with uniform density ρ. The center of mass

Area under curve, Write a program to find the area under the curve y = f(x)...

Write a program to find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. The area under a curve between two points can b

Surface areas and volumes, a conical vessel of radius 6cm and height 8cm is...

a conical vessel of radius 6cm and height 8cm is completely filled with water.a sphere is lowered into the water and its size is such that when it touches the size it is immersed.w

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd