Question

Hello!
Que. Find a quadratic polynomial, whose zero are -3 and 4.
The answer in book is xsquare/2 - x/2 -6
Kindly help me and give full explanation of the topic.
: )

Answer 1

To form quadratic equation,

x²-(-3+4)x+(-3×4)
x²-(1)x+(-12)
x²-x-12
now dividing by 2 we get,
x²/2 -x/2 -6

hope this helps :-)

Answer 2

Here is the solution :

In General, if the roots of the quadratic equations are a and b, then the Quadratic equation will be :

x² - (a+b)x + ab = 0,

Given that,

Roots are, -3 and 4,
So, let a = -3 and b = 4,

=> Sum of the roots = -3 + 4 = 1,
=> Product of the roots = -3 * 4 = -12,

Now, From the above statement we can write the Quadratic Equation as,

x² -(1)x -12 =0,
=> x² -x -12 = 0,

This is the answer, 

Now, Let me tell you something !
The answer given the book and the answer you got are same !

Divide our answer by 2 on both sides,

=> (x²)/2 - (x)/2 - (12)/2 = 0,
=> (x²)/2 - (x)/2 - 6 = 0,

See, Both are same, I don't know why exacly they have divided the equation by 2 on both sides ! But what you got is also right !

Therefore : the answer is x² - x - 12 =0 (or) x²/2 - x/2 - 6 =0,

Conclusion : Both are same, Don't worry ! It's just looks something different but what you got is correct :) !!

Hope you understand, Have a Great Day !
Thanking you, Bunti 360 !!