Find the roots of the quadratic equation?

Question

Find the roots of the quadratic equation
x^2 - 11x + 28 = 0

If there is more than one root, then write all of them.

Answer 1

x^2 - 11x + 28 = 0

This factors easily. The two numbers that multiply to make 28 and add to make -11 are -7 and -4, so this factors as

(x - 7)(x - 4) = 0

Meaning

x = 7, 4

Answer 2

Given equation is x^2 - 11x + 28 = 0
Now consider the factors of the constant value such that when they are added or subtracted we get 11 as the value

so 7 * 4 = 28 and 7 + 4 = 11 can be considered
be careful sometimes we may get 2 or more pairs like the same thing then we have to use all of them and check which one leads to answer

now x^2 -4x -7x +28=0 (here split 11 in terms of the factors)

take x as common from 1st part
and 7 as common from 2nd part

x(x-4)-7(x-4)=0
here we must see that (x-4) should be present in both parts

(x-7)(x-4)=0
now equate both equations seperately to 0

x-7=0 x-4=0
x=7 x=4

so 7 and 4 are the roots of quadratic equation

the above described method is one method
we have one method that is

if the equation is in form ax^2 + bx + c = 0

Then the roots can be found out using the formula

x = (-b + (b^2 -4ac)^1/2 )/2a or (-b - (b^2 -4ac)^1/2 )/2a

so here in given equation we have
a=1
b=-11
c=28
now if we apply in the above formula

x=(11+(11^2-(28*4*1))^1/2))/2*1

=(11+(121-112)^1/2))/2

=(11+(9)^1/2)/2

=(11+3)/2

=7

x=(11-(11^2-(28*4*1))^1/2))/2*1

=(11-(121-112)^1/2))/2

=(11-(9)^1/2)/2

=(11-3)/2

=4

so roots are 7 and 4

now did u get it!
bye

Answer 3

The roots are 4 & 7; i.e. x=4 & x=7.

In algebra, the middle term is the sum of the two 4 + 7 = 11; and the last term is the product of the two 4 x 7 = 28.

(x-4) (x-7) = x*2 - 11x + 28 = 0.

Hence, x=4 and x =7.

When you are already familiar with algebra, this quadratic equation will appear very simple and you can solve it visually.

Just inspect the middle term and the last term for the sum and product, respectively.

Answer 4

perhaps you fairly recommend: The roots of the quadratic equation 16x^2+7x+4=0 are ?² and ?². Then the equation sixteen(a million/x)^2+7(a million/x)+4=0 has the roots a million/?² and a million/?². This equation could properly be rearranged into the quadratic 4x^2+7x+sixteen=0.

Answer 5

By inspection, the roots are 4 and 7. Those are the two numbers whose sum is 11 and product is 28.

Answer 6

x = 11 or x = -28

Answer 7

By using inspection method,
x^2 - 11x + 28 = 0
(-x + 4)(-x + 7) = 0

(-x + 4) = 0
-x = -4
x = 4

OR

(-x + 7) = 0
-x = -7
x = 7

Therefore, x = 4, 7 (final answer)

Answer 8

x^2 - 11x + 28 = 0 breaks down into (x-7) * (x-4)=0

then slove for x in each equation, you get x = 7 or 4

hope this helps

Answer 9

Puggy's answer is correct you factor then the number needed to get 0 equals your roots. To check you answer just FOIL the factors and you should get the original equation again.

Answer 10

I think it should be -4 and -7.